A water tank is a cylinder with radius 40 cm and depth 150 m
150 cm
40 cm
It is filled at the rate of 0.2 litres per second.
1 litre = 1000 cm3
Does it take longer than 1 hour to fill the tank?
​

The volume of a cylinder with radius [tex]r[/tex] and height [tex]h[/tex] is

[tex]V=\pi r^2h[/tex]

Differentiate both sides with respect to time:

[tex]\dfrac{\mathrm dV}{\mathrm dt}=2\pi rh\dfrac{\mathrm dr}{\mathrm dt}+\pi r^2\dfrac{\mathrm dh}{\mathrm dt}[/tex]

We're given that

[tex]\dfrac{\mathrm dr}{\mathrm dt}=6\dfrac{\rm in}{\rm s}[/tex]

[tex]\dfrac{\mathrm dh}{\mathrm dt}=-3\dfrac{\rm in}{\rm s}[/tex]

so that at the point when [tex]r=5\,\rm in[/tex] and [tex]h=11\,\rm in[/tex], the volume is undergoing a total change of

[tex]\dfrac{\mathrm dV}{\mathrm dt}=2\pi(5\,\mathrm{in})(11\,\mathrm{in})\left(6\dfrac{\rm in}{\rm s}\right)+\pi(5\,\mathrm{in})^2\left(-3\dfrac{\rm in}{\rm s}\right)[/tex]

[tex]\boxed{\dfrac{\mathrm dV}{\mathrm dt}=585\pi\dfrac{\mathrm{in}^3}{\rm s}}[/tex]

The volume of the right circular cylinder is changing at a rate of 255π cubic inches/sec with the radius increasing at 6 in./s and height decreasing at 3 in./s.

The question involves the application of calculus concepts particularly related to volume flow rate. The volume (V) of a right circular cylinder is given by V = πr²h, where r is the radius and h is the height. We can take the derivative in respect to time (t) of both sides, which will result in dV/dt = πrh(dr/dt) + πr²(dh/dt).

According to the problem, dr/dt = 6 in./s and dh/dt = -3 in./s. The volume is changing when the radius (r) is 5 in. and the height (h) is 11 in. Substituting all these values into the formula, we get: dV/dt = π(5)(11)(6) + π(5)²(-3). This equals 330π - 75π = 255π cubic inches/sec.

Thus, the volume of the cylinder is changing at a rate of 255π cubic inches/sec.

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Answer:

Hence final answer is [tex](1,3)[/tex].

correct choice is D because both ends are open circles.

Step-by-step explanation:

Given inequality is [tex]\frac{x-1}{x-3}<0[/tex]

Setting both numerator and denominator =0 gives:

x-1=0,  x-3=0

or x=1, x=3

Using these critical points, we can divide number line into three sets:

[tex](-\infty,1)[/tex], [tex](1,3)[/tex] and [tex](3,\infty)[/tex]

We pick one number from each interval and plug into original inequality to see if that number satisfies the inequality or not.

Test for [tex](-\infty,1)[/tex].

Clearly x=0 belongs to [tex](-\infty,1)[/tex] interval then plug x=1 into [tex]\frac{x-1}{x-3}<0[/tex]

[tex]\frac{0-1}{0-3}<0[/tex]

[tex]\frac{-1}{-3}<0[/tex]

[tex]\frac{1}{3}<0[/tex]

Which is False.

Hence [tex](-\infty,1)[/tex] desn't belongs to the answer.

Similarly testing other intervals, we get that only [tex](1,3)[/tex] satisfies the original inequality.

Hence final answer is [tex](1,3)[/tex].

correct choice is D because both ends are open circles.

Answer:

Step-by-step explanation:

x% of y equals to 0.01*x*y

Just put the numbers in the formula

33% of 507 = 167.31

48% of 375 = 180

76% of 285 = 216.6

60% of 398 = 238.8

89% of 150 = 133.5

26% of 430 = 111.8

81% of 216 = 174.96

5% of 584 = 29.2

18% of 725 = 130.5

2% of 115 = 2.3

90% of 152 = 136.8

12% of 649 = 77.88

55% of 216 = 118.8

43% of 108 = 46.44

97% of 235 = 227.95

x = 0, -1, -2

When the function is set equal to zero and solved for, you end up with these three numbers.

Answer:

b

Step-by-step explanation:

Based on the rate at which the population is decreasing, we can calculate that population in 2008 is A. 1,200 people

The population after a certain number of years is:

= Population now x (1 - rate) ^ number of years

The number of years is:

= 2008 - 2000

= 8 years

The population in 2008 is therefore:

= 1,300 x ( 1 - 1%)⁸

= 1,199.57

= 1,200 people

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Answer: I would just say add a line to the Equal sign so the equation would read

5+5+5≠550, since this way it would say that 5+5+5 ISNT equal to 550 which is technically true, but that might be wrong.

QA) Which solid figures can the staircase be broken into?

A) The staircase can be broken into 3 rectangular prisms.

QB) What are the dimensions of each solid figure?

A) We are given the height (2.5 ft) and the length (3 ft) of the entire staircase. To find the height and length of each step, just divide by 3:

2.5 / 3 = 5/6 ft high

3 / 3 = 1 ft long

Looking at the image given, we can see that the staircase is 6 ft wide.

Bottom prism: 3 ft long, 6 ft wide, and 5/6 ft high.

Middle prism: 2 ft long, 6 ft wide, and 5/6 ft high.

Top prism: 1 ft long, 6 ft wide, and 5/6 ft high.

QC) How much concrete will be needed to form the staircase?

A) To answer this question, we have to find the volume of each rectangular prism. The formula for the volume of a rectangular prism is

V = lwh; where l = length, w = width, and h = height.

We need to apply this formula to each prism. I'll go from the bottom up.

(1.) V = lwh; l = 3, w = 6, h = 5/6

V = (3)(6)(5/6)

V = 15 ft²

(2.) V = lwh; l = 2, w = 6, h = 5/6

V = (2)(6)(5/6)

V = 10 ft²

(3.) V = lwh; l = 1, w = 6, h = 5/6

V = (1)(6)(5/6)

V = 5 ft²

To find the amount of concrete needed to form the staircase, just add the volumes of the three rectangular prisms:

15 + 10 + 5 = 30 ft²

The contractor will need enough concrete to cover 30 ft² to form the staircase.

Hope this helps!

Final answer:

The staircase can be broken into rectangular prisms, each representing a step. The volume of each step is calculated using the given dimensions, which are then summed to find the total concrete needed.

Explanation:

To determine the amount of concrete needed to form a staircase, we need to calculate the volume of concrete required for each step and then sum them up. Since each step is of the same size, we can break down the staircase into a set of rectangular prisms, where each prism represents a step.

Dimensions of each solid figure (step): Given a stage height of 400 mm and 3 steps, the height of each step would be 400 mm / 3, which is around 133.33 mm or 13.33 cm. The length of the horizontal part of each step is 800 mm or 80 cm. Assuming a step width of 1,200 mm or 120 cm (since the steps must be wide enough for two people), we obtain the dimensions for each step.

To calculate the volume of each step, we use the formula for the volume of a rectangular prism: Volume = Length × Width × Height. Therefore, we have Volume = 80 cm × 120 cm × 13.33 cm for each step. To find the total volume for the staircase, we multiply the volume of one step by the number of steps (3 in this case).

Calculating the total concrete required: After finding the volume of one step, we multiply it by 3 (since there are 3 steps) to find the total concrete needed.

Answer:

Donuts cost $2.00 and Cookies cost $1.50

Step-by-step explanation:

D = cost of a donut

C = cost of a cookie

4D + 10C = $23.00

8D + 6C = $25.00

Eliminate a variable when subtracting the two equations.  Change both values with C to 60 in order to eliminate the C variable and solve for D.

80D + 60C = $250.00 subtracted from 24D + 60C = $138

56D = $112.00  (Divide by 56 to single out the variable)

56D/56 = $112.00/56

D = $2.00

Use the D value to solve for C.

4(2) + 10C = $23.00

8 + 10C = $23.00

8 - 8 + 10C = $23.00 - 8

10C = $15.00

10C/10 = $15/10

C = $1.50

Check:

Bentley:  

4D + 10C = $23

4(2) + 10(1.50) = $23

8 + 15 = $23

23 = 23

Skylar:

8D + 6C = $25

8(2) + 6(1.50) = $25

16 + 9 = $25

25 = 25

Answer:

Each donut costs $2 and each cookie costs $1.5

Step-by-step explanation:

1. Let´s name the variables as the following:

x = price of one donut

y = price of one cookie

2. Write in an equation form which Bentley bought:

[tex]4x+10y=23[/tex] (Eq.1)

3. Write in an equation form which Skylar bought:

[tex]8x+6y=25[/tex] (Eq.2)

4. Solve for x in Eq.1:

[tex]4x+10y=23[/tex]

[tex]4x=23-10y[/tex]

[tex]x=\frac{23-10y}{4}[/tex] (Eq.3)

5. Replace Eq.3 in Eq.2 and solve for y:

[tex]8*(\frac{23-10y}{4})+6y=25[/tex]

[tex]\frac{184-80y}{4}+6y=25[/tex]

[tex]\frac{184-80y+24y}{4}=25[/tex]

[tex]184-80y+24y=100[/tex]

[tex]-80y+24y=100-184[/tex]

[tex]-56y=-84[/tex]

[tex]y=\frac{84}{56}[/tex]

[tex]y=1.5[/tex]

6. Replacing the value of y in Eq.3:

[tex]x=\frac{23-10*(1.5)}{4}[/tex]

[tex]x=\frac{23-10*(1.5)}{4}[/tex]

[tex]x=\frac{23-15}{4}[/tex]

[tex]x=\frac{8}{4}[/tex]

[tex]x=2[/tex]

Therefore each donut costs $2 and each cookie costs $1.5

Answer:

[tex]5(a^2b-a^2c-db+dc)[/tex]

Step-by-step explanation:

Given expression is [tex]5a^2b- 5a^2c -5db +5dc[/tex].

Now we need to show the first step of factoring.

We know that first step of factoring in any problem is to find the GCF that is find the greatest common factor. We see that 5 is the only largest number that can divide each term so 5 is the GCF.

Now we write 5 outside parenthesis and divide given terms by 5 to find the terms that goes inside parenthesis.

Hence first step of factoring is given by :

[tex]5a^2b- 5a^2c -5db +5dc[/tex]

[tex]=5(a^2b-a^2c-db+dc)[/tex]

The first step when factoring [tex]\(5a^2b - 5a^2c - 5db + 5dc\)[/tex] by grouping is to group the terms and then factor out the common terms from each group

Let's factor the expression [tex]\(5a^2b - 5a^2c - 5db + 5dc\)[/tex] by grouping.

First, let's group the terms:

[tex]\( (5a^2b - 5a^2c) + (-5db + 5dc) \)[/tex]

Now, let's factor out the common terms from each group:

[tex]\( 5a^2(b - c) + 5d(-b + c) \)[/tex]

Now, we can factor out the common factor of 5 from both terms:

[tex]\( 5(a^2(b - c) + d(-b + c)) \)[/tex]

So, the factored expression is [tex]\(5(a^2(b - c) + d(-b + c))\).[/tex]

In the given expression, we have four terms[tex]: \(5a^2b\), \(-5a^2c\), \(-5db\), and \(5dc\).[/tex]

The first step in factoring by grouping is to group the terms in pairs. Here, we pair [tex]\(5a^2b\)[/tex] with [tex]\(-5a^2c\)[/tex] and [tex]\(-5db\)[/tex] with [tex]\(5dc\).[/tex]

Next, we factor out the common terms from each group. From the first group, we factor out [tex]\(5a^2\)[/tex], and from the second group, we factor out [tex]\(5d\).[/tex] This leaves us with [tex]\(b - c\)[/tex] in the first group and [tex]\(-b + c\)[/tex] in the second group.

Finally, we factor out the common factor of 5 from both terms to get the final factored expression [tex]\(5(a^2(b - c) + d(-b + c))\).[/tex]

So, the first step when factoring [tex]\(5a^2b - 5a^2c - 5db + 5dc\)[/tex] by grouping is to group the terms and then factor out the common terms from each group.

Complete question:

show the first step when factoring [tex]5a^2b- 5a^2c -5db +5dc[/tex] by grouping?

Answer:

Both A and B

Step-by-step explanation:

A = {(3, −5), (4, 6), (−3, 9), (2, 7)}  

-Each x goes to a different y so this is a function

B = {(2, 4), (−1, −7), (5, 6), (4, 3)}

-Each x goes to a different y so this is a function

Answer:

three hundred

Step-by-step explanation:

Answer:

300

Step-by-step explanation:

5,9 times 540

Answer:

21503 feet²

Step-by-step explanation:

Area of Square 1 = 69 x 69 = 4761

Area of Triangle = 69 x 92 ÷ 2 = 3174

Area of Square 2 = 92 x 92 = 8464

Area of Circle = 57.5² x π ÷ 2 ≈ 5104

Total Area = 21503

solution for #18 is C and for #19 is D

QUESTION 18

Use the Pythagorean Identity.

[tex] \cos^{2}( \theta) +\sin^{2}( \theta) = 1[/tex]

We substitute the given value into the formula,

[tex] \cos^{2}( \theta) +( { \frac{4}{7} })^{2} = 1[/tex]

[tex] \cos^{2}( \theta) + \frac{16}{49} = 1[/tex]

[tex] \cos^{2}( \theta) = 1 - \frac{16}{49} [/tex]

[tex]\cos^{2}( \theta) = \frac{33}{49} [/tex]

Since we are in the first quadrant, we take positive square root,

[tex]\cos( \theta) = \sqrt{\frac{33}{49} } [/tex]

[tex]\cos( \theta) = \frac{ \sqrt{33}}{7} [/tex]

The 3rd choice is correct.

QUESTION 19.

We want to simplify;

[tex]18 \sin( \theta) \sec( \theta) [/tex]

Recall the reciprocal identity

[tex] \sec( \theta) = \frac{1}{ \cos( \theta) } [/tex]

This implies that,

[tex]18 \sin( \theta) \sec( \theta) =18 \sin( \theta) \times \frac{1}{ \cos( \theta) } [/tex]

[tex]18 \sin( \theta) \sec( \theta) =18 \times \frac{\sin( \theta) }{ \cos( \theta) } [/tex]

This will give us:

[tex]18 \sin( \theta) \sec( \theta) =18 \tan( \theta) [/tex]

The correct choice is D.

ANSWER

x=100,y=10

EXPLANATION

The given logarithmic equations are;

[tex] log_{10}( {x}^{2} {y}^{3} ) = 7[/tex]

This implies that,

[tex] {x}^{2} {y}^{3} = {10}^{7} ...(1)[/tex]

and

[tex] log_{10}( \frac{x}{y} ) = 1[/tex]

This implies that,

[tex] \frac{x}{y} = {10}^{1} [/tex]

[tex]x = 10y...(2)[/tex]

Put equation (2) into equation (1)

[tex]{(10y)}^{2} {y}^{3} = {10}^{7}[/tex]

[tex]10 ^{2} y^{2} {y}^{3} = {10}^{7}[/tex]

[tex]{y}^{5} = {10}^{5}[/tex]

Hence y=10.

This implies

[tex]x = 10(10) = 100[/tex]

Answer:

The top isn't closed.

Step-by-step explanation:

The bottom is enclosed, creating more surface area, but the top is opened.

Answer:

The surface area of a cylinder is given by :

SA=[tex]2 \pi rh+2\pi r^{2}[/tex]

When the base is same but the height is doubled. Doubling the height replaces h with 2h:

New formula becomes:

SA=[tex]2 \pi r(2h)+2\pi r^{2}[/tex]

SA = [tex]4\pi rh+2\pi r^{2}[/tex]

We can see that only the height is doubled not the radius. The formula changes a little bit.

We can take an example-

Lets say the height of cylinder is 10 cm and radius is 4 cm

So, SA in 1st case :

SA=[tex]2\times3.14\times4\times10+ 2\times3.14\times (4)^{2}[/tex]

=[tex]251.2+100.48=351.68[/tex] cm square

SA in 2nd case:

[tex]4\times3.14\times4\times10+ 2\times3.14\times(4)^{2}[/tex]

= [tex]502.4+100.48=602.88[/tex] cm square

We can see that area of lateral surface doubles up in case 2 but the base area remains the same.

Answer:

x = -48, y = 25

Step-by-step explanation:

Both equations have a 5y term, we can work with that.

Let's first convert them into 5y = ... form:

2x + 5y = 29 => 5y = 29 - 2x

3x + 5y = -19 => 5y = -3x - 19

Now we can equate the right-hand sides:

29 - 2x = -3x - 19

And simplify:

29 + 19 = -3x + 2x => x = -48

Let's put this x value in the first:

2*(-48) + 5y = 29 =>

-96 - 29 = -5y =>

-5y = -125 =>

y = 25

ANSWER

The value of x is 47°

EXPLANATION

PQ is a tangent to the circle at Q.

This tangent meets the diameter at 90°.

The sum of interior angles of a triangle is 180°

This implies that:

[tex]90 \degree + x + 43 \degree = 180 \degree[/tex]

[tex]133 \degree + x = 180 \degree[/tex]

Group similar terms to obtain;

[tex] x = 180 \degree - 133 \degree[/tex]

Simplify similar terms to get;

[tex]x = 47\degree[/tex]

Answer:

The value of x = 47°

Step-by-step explanation:

From the figure we can see that a circle with center O.

PQ is a tangent to the circle fro point P.

m<P = 43°

Therefore <Q = 90°

To find the value of x

From the given triangle we can write,

x + m<Q + m<P = 180

x = 180 - (m<Q + m<P)

 = 180 - (90 + 43)

 = 180 - 133 = 47°

Therefore the value of x = 47°

ANSWER

9

EXPLANATION

We want to find the distance between the points (3, -5) and (-6, -5).

The given points have the same y-coordinates .

This means it is a horizontal line.

We use the absolute value method to find the distance between the two points.

We find the absolute value of the distance between the x-values.

The distance between the two points is

|3--6|=|3+6|=|9|=9

Answer:b

Step-by-step explanation:

Answer:

The safe dose for the child is:   [tex]640\ \frac{mg}{day}[/tex]

Step-by-step explanation:

We know that the conversion factor is 40 mg/kg/day

The child weighs 16 kg. This means that 40 mg per day corresponds to each kilogram of the child.

So to know how many milligrams per day correspond per day we must multiply 16 kg by the conversion factor

[tex]16\ kg * 40\ \frac{\frac{mg}{kg}}{day} = 640\ \frac{mg}{day}[/tex]

Answer:

The safest dose would be 640 mg per day.

Hope this helps!

Answer:

Step-by-step explanation:

[tex]Q+p+Q+p+Q\\\\\text{combine like terms}\\\\=(Q+Q+Q)+(p+p)=3Q+2p[/tex]

The answer is:

The second option,

b.) [tex]C(x)=40.60x+201[/tex]

We are given the functions E(x) and K(x), since they both are function of the same variable, we need to add them in order to find the correct option.

From the statement we know the functions:

[tex]E(x)=22.75x+74[/tex]

and

[tex]K(x)=17.85x+127[/tex]

So, adding the functions we have:

[tex]C(x)=E(x)+F(x)[/tex]

[tex]C(x)=(22.75x+74)+(17.85x+127)[/tex]

[tex]C(x)=22.75x+17.85x+74+127[/tex]

[tex]C(x)=40.60x+201[/tex]

Hence, the answer is the second option,

b.) [tex]C(x)=40.60x+201[/tex]

Have a nice day!

Answer:

The answer is b

Step-by-step explanation:

C(x)=40.60x + 201

Answer:

[tex]\frac{7\pi }{2}[/tex]

Step-by-step explanation:

Given

sin x = - 1

x = [tex]sin^{-1}[/tex] ( - 1 )

  = [tex]\frac{3\pi }{2}[/tex] + 2kπ k ∈ Z

For 2π < x < 4π, then

x = [tex]\frac{7\pi }{2}[/tex]

Answer:

3π/13

Step-by-step explanation:

In order to find the reference angle of a given angle, first of all, its quadrant is determined

In order to determine the quadrant,

10π/13=10(180)/13

=138.46

As the given angle belongs to 2nd quadrant, it will be subtracted from 180 degrees also denoted by pi.

So,

Reference angle for 10π/13= π-10π/13

=(13π-10π)/13

=3π/13

So the reference angle for 10π/13 is 3π/13 ..

The collection of investments in a mutual fund is referred to as a portfolio, which can include a variety of stocks and bonds. Index funds are examples of mutual funds that track the performance of market indexes. Mutual funds are significant in the financial landscape, with many U.S. households investing in them.

The collection of investments in a mutual fund is called a portfolio.

Mutual funds gather stocks or bonds from various companies into one investment vehicle, making it simpler for investors to own a diversified collection without purchasing each security individually.

Investors purchase shares of the mutual fund and receive returns based on the collective performance of the fund's portfolio.

For instance, index funds are types of mutual funds that aim to mimic the performance of a specific market index.

This strategy offers broad market exposure and low operating expenses.

There are also specialized mutual funds that focus on particular sectors or regions, offering different levels of risk and potential return.

In the modern financial landscape, mutual funds play a significant role, with a substantial percentage of U.S. households holding investments in these funds.

Step-by-step explanation:

(B).(x=5 or -5) is the homogeneous mixture

The first equation has two distinct rational solutions, the expression 2x - 1 can be one of the factors to solve the second equation, the solutions to the third equation are x = -2/5 and x = 0, and the solutions to the fourth equation are x = -1 and x = -5.

1. To find the solutions to the equation x^2 - 1 = 24, we can start by isolating the squared term:

x^2 = 24 + 1

x^2 = 25

Next, we take the square root of both sides to find the values of x:

x = ±√25

Therefore, there are two distinct rational solutions to the equation.

2. In order to solve the quadratic equation 2x^2 - 7x + 3 = 0, Marcus can use the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a). One of the factors he can write is 2x - 1.

3. The solutions to the equation 5x^2 = -2x are found by getting all the terms to one side and setting the equation equal to zero:

5x^2 + 2x = 0

Next, we factor out the greatest common factor:

x(5x + 2) = 0

Setting each term equal to zero, we get two values for x:

x = 0 or x = -2/5

Therefore, the statement that the solutions are x = -2/5 and x = 0 is true.

4. To find the solutions to the equation (x + 3)^2 - 4 = 0, we isolate the squared quantity:

(x + 3)^2 = 4

Next, we take the square root of both sides, considering both the positive and negative square roots:

x + 3 = ±√4

x + 3 = ±2

Solving for x, we get two solutions:

x = -3 - 2 = -5

x = -3 + 2 = -1

Therefore, the statement that the solutions are x = -1 and x = -5 is true.

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Answer:

3C + 5 T = 550

C+T= 122

PUT IN 1  T= 122-C

3C + 5 (122-C)=550

3C -5C + 610=550

-2C= 550 - 610= -30

C= 15

T= 122-15 = 107

Step-by-step explanation:

Answer:  50

Step-by-step explanation:

Let x be the number of cars and y be the number of trucks .

By considering the given information, we get

[tex]x+y=122-----------------(1)\\\\3x+5y=510-------------------(2)[/tex]

Multiply (1) by 3 , we get

[tex]3x+3y=366--------------(3)[/tex]

Eliminate equation (3) from (2), we get

[tex]2y=144\\\\\Rightarrow\ y=72[/tex]

Put y= 72 in equation (1), we get

[tex]x+72=122\\\\\Rightarrow\ x=122-72=50[/tex]

Hence, the number of cars did the club = 50

Answer:

$10.50

Step-by-step explanation:

The first step is to determine the cost per student for the trip.

It cost $443.75 for 25 students, so

TS = 443.75 / 25 = $17.75 per student.

From that $17.75, we know we should remove $7.25 for the lunch in order to get the entrance fee:

EF = 17.75 - 7.25 = 10.50

The entrance fee for one student was $10.50

Answer:

(5,0)

Step-by-step explanation:

Count how many units are there on the x-axis first and in this case it is 5 the count how many on the y axis (going up or down) and that is 0 so then use this for the coordinate: (x,y)=(5,0)

Answer:

(5,0)

Step-by-step explanation:

Count how many units are there on the x-axis first and in this case it is 5 the count how many on the y axis (going up or down) and that is 0 so then use this for the coordinate: (x,y)=(5,0)

Answer:

1.  $640

2. About 10.3 years later

Step-by-step explanation:

This is a compound decay problem. The formula is

[tex]F=P(1-r)^t[/tex]

Where

F is the future amount

P is the initial amount

r is the rate of decrease (in decimal), and

t is the time in years

Question 1:

We want to find F after 2 years of a phone initially costing 1000. So,

P = 1000

r = 20% or 0.2

t = 2

plugging into the formula, we solve for F:

[tex]F=P(1-r)^t\\F=1000(1-0.2)^2\\F=1000(0.8)^2\\F=640[/tex]

The phone is worth $640 after 2 years

Question 2:

We want to find when will the phone be worth 10% of original.

10% of 1000 is 0.1 * 1000 = 100

So, we want to figure this out for future value of 100, so F = 100

We know, P = 1000 r = 0.2 and t is unknown.

Let's plug in and solve for t (we need to use logarithms):

[tex]F=P(1-r)^t\\100=1000(1-0.2)^t\\100=1000(0.8)^t\\\frac{100}{1000}=0.8^t\\0.1=0.8^t\\ln(0.1)=ln(0.8^t)\\ln(0.1)=t*ln(0.8)\\t=\frac{ln(0.1)}{ln(0.8)}\\t=10.32[/tex]

So, after 10.32 years, the phone would be worth less than 10% of original value.