suppose you deposit $25,000 in to a fund for which the annual interest rate is 5.3% compounded continuously. find the number of years it will take to double in value (round your answer to the nearest tenth of a year)

Answers

Answer 1

so, the principal is 25,000, when it double then, the accumulated amount is 50,000.

[tex]\bf \qquad \textit{Continuously Compounding Interest Earned Amount}\\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\to &\$50000\\ P=\textit{original amount deposited}\to& \$25000\\ r=rate\to 5.3\%\to \frac{5.3}{100}\to &0.053\\ t=years \end{cases} \\\\\\ 50000=25000e^{0.053t}\implies \cfrac{50000}{25000}=e^{0.053t}\implies 2=e^{0.053t} \\\\\\ ln(2)=ln(e^{0.053t})\implies ln(2)=0.053t\implies \cfrac{ln(2)}{0.053}=t \\\\\\ 13.0782486898102888\approx t\implies 13.08\approx t[/tex]

Related Questions

select the graph that represents the given set a={(1,2),(2,3),(3,4),(4,5)

Answers

y=x+1 is the equation for the graph

An interior angle and an exterior angle are adjacent. The interior angle measures 84°. What is the measure of the exterior angle?

Answers

adjacent angles are supplementary

so the exterior angles = 180 - 84 = 96 segrees.

The measure of the exterior angle is

What is Exterior Angle?

External angles are those that run parallel to a polygon's inner angles but are located outside of it. The sum of the two internal opposed angles determines the size of an outside angle.

We have,

The interior angle measures 84°.

We know that

Exterior angle + interior angle = 180

Exterior angle = 180 - Interior angle

Exterior angle = 180 - 84

Exterior angle = 96

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how to solve an equation for x with natural log of x

Answers

Question is not specific, so can only give a general answer.
As an example:
If the equation is of the form
log(x)=5
then raise each side to the power of e to give
e^(log(x))=e^5
Since e^(log(x))=x, we have
x=e^5.

A logarithmic equation involving natural logarithms can be solve by taking the exponent of both sides

How to solve a natural logarithmic equation for x

To solve an equation involving the natural logarithm of x, you generally follow these steps:

Isolate the natural logarithm termExponentiate both sidesSolve for x: After removing the natural logarithm, solve the resulting equation for x.

Take for instance, the equation is of the form

2 + ln(x) = 7

Isolate the natural logarithm

ln(x) = 5

Take the exponent of both sides

So, we have

[tex]x = e^5[/tex]

Evaluate the exponent

x = 148.41

Hence, the logarithmic equation solved for x is x = 148.41

x+29=−11

what does X equal

Answers

x+29=-11
-29 -29

x = -40

X+29= -11
29 - 29 = 0
0 - (-11) = -11
-29 + -11 = -40
-40 + 29 = -11

Determine whether the fractions -4/5, -4/6, -4/7, and -4/8 are arranged in order from least to greatest. explain

Answers

They are ordered least to greatest

Which of the following is a sample of the population of bookstores on the West Coast of the United States? I. All book stores in California II. Randomly selected children's book stores III. Internet book stores A. I only B. II only C. I and III D. III only E. I and II

Answers

Eliminate (I) "all bookstores in California," because we're choosing a SAMPLE, not an entire population of stores.

Keeping this in mind, we'd not choose "Internet bookstores" unless it's clear that we're sampling these stores, not looking at all of them.

This leaves only "randomly selected children's bookstores." Even now I'm not comfortable, because this choice focuses specifically on children's stores (instead of on bookstores in general).

Answer:

It would be I - All bookstores in California

Step-by-step explanation:

Internet book stores and random children's bookstores do not specify that they're on the West Coast and could be taken from anywhere

Deanna has 80 books in her collection. If 60% of the books are fiction, how many of the books are nonfiction?

Answers

if 60% is fiction, then 40% are non fiction

80 x 40% =

80 x 0.40 = 32

32 books are nonfiction

Which BEST describes the construction of a triangle if given one side length of 10 cm and one right angle?
A)
Unique triangle

B)
More than one triangle

C)
Triangle not possible

D)
Cannot be determined

Answers

B, is the answer! :))))))))))))))

Answer:

Step-by-step explanation:

Th local park has 4 bike racks. Each bike rack can hold 15 bikes. There are 16 bikes in the bike racks. What expression shows the total number of empty spaces in the bike racks?

Answers

4 * 15 bike storage capacity

16 spaces are occupied

This leaves 60 - 16, or 44, spaces available.

How to find the derivative of functions: y=(5x+7)(x+5)^3

Answers

Use the product and chain rules.

We want dy/dx.

dy/dx = (5x+7)(x+5)^3

dy/dx = (5x+7)3(x+5)^2 + (x+5)^3 (5)

We now simplify as much as possible.

dy/dx = 3(5x+7)(x+5)^2 + 5(x+5)^3

The volume of this rectangular prism is 6x3. What does the coefficient 6 mean in terms of the problem?

A. The total volume of the prism is 6 cubic units.
B. The length is 6 times the width.
C. The width is 6 times the height and the length.
D. The length of the prism is 6 units.

Answers

Answer:

B. The length is 6 times the width

Step-by-step explanation:

The proper solution is choice B. The length is 6 times the width.

How do you resolve rectangular prisms?

To find the quantity of a rectangular prism, multiply its 3 dimensions: duration x width x height. The volume is expressed in cubic gadgets.

What are examples of square prisms?

Right rectangular prisms or cuboids are all around us. a few examples are books, packing containers, homes, bricks, forums, doorways, containers, cabinets, mobiles, and laptops.

What does the coefficient mean?

Any of the elements of a product taken into consideration with regards to a specific element particularly: a constant thing of a term as outstanding from a variable.

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Jerry lost his credit card and instead of reporting it right away, he decides to continue looking for it believing he could find it. Some time passes and after two weeks, he logs into the account activity page of his credit card and sees a recent $500 internet purchase that was made by someone else. At that moment, he calls to report his card stolen. How much of this $500 charge is Jerry at risk for having to pay?

Answers

Jerry did not report his lost credit card right away believing that he could find it. Fraudulent transactions were made on his account and he is responsible to pay the maximum amount of $50 under the Fair Credit Billing Act (FCBA).

Translate the phrase to mathematical language. Then simplify the expression.

Subtract 81 from −55.
What is a numerical expression for the phrase?__
(Do not simplify.)

Simplify the expression.__

Answers

"Subtract 81 from −55" can be written symbolically as (-55) - 81.

Simplifying, -55-81 = - 136

A cafe only sells two types of sandwiches, turkey, and steak. The cafe charges $4 for turkey sandwiches and $6 for steak sandwiches. Last month, the cafe sold $4524 worth of sandwiches. The cafe sold a total of 925 sandwiches.

How many turkey sandwiches did they sell?

Answers

t + s = 925....s = 925 - t
4t + 6s = 4524

4t + 6(925 - t) = 4524
4t + 5550 - 6t = 4524
-2t = 4524 - 5550
-2t = -1026
t = 1026/2
t = 513 <== 513 turkey sandwiches

t + s = 925
513 + s = 925
s = 925 - 513
s = 412 <=== 412 steak sandwiches

Answer:

They sold 513 turkey sandwiches.

Step-by-step explanation:

Let t be the number of turkey sandwiches and s be the number of steak sandwiches.

With these variables, we can create equations for the totals they've given us:

Total sandwiches = [tex]t+s=925[/tex]

Total income = [tex]4t+6s=4524[/tex]

Now we can solve the system for the number of turkey sandwiches and steak sandwiches

Isolate t for [tex]t+s=925[/tex] => [tex]t=925-s[/tex]Substitute [tex]t=925-s[/tex] into [tex]4t+6s=4524[/tex]

[tex]4\left(925-s\right)+6s=4524[/tex]

Solve for s

[tex]3700-4s+6s=4524\\3700+2s=4524\\3700+2s-3700=4524-3700\\2s=824\\\frac{2s}{2}=\frac{824}{2}\\s=412[/tex]

For [tex]t=925-s[/tex] substitute s = 412

[tex]t=925-412\\t=513[/tex]

They sold 513 turkey sandwiches and 412 steak sandwiches.

FREE POINTS!!!!!!!!!! 10 POINTS Len's recipe for blueberry muffins calls for 110.25 grams of brown sugar for the muffin batter and an additional 55.45 grams of brown sugar for the topping. Len wants to make 4.5 batches of muffins. Enter the total amount of brown sugar that Len will need

Answers

Wow.... My brother Said that it took him a while to figure it out... but

add 110.25 and 55.45

you would get 165.70

multiply 165.70 by 4.5

then you would get 745.65

745.65 is your answer

the answer is 745.65

hope i helped:)

Suppose a parabola has a vertex (5,-3) and also passes through (6,1). Write the equation of the parabola in vertex form

Answers

so hmmmm let's assume is a vertical parabola, so, the squared variable will then be the "x".

[tex]\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ \begin{cases} h=5\\ k=-3 \end{cases}\implies y=a(x-\stackrel{h}{5})^2\stackrel{k}{-3} \\\\\\ \textit{now, we also know that } \begin{cases} x=6\\ y=1 \end{cases}\implies 6=a(1-5)^2-3 \\\\\\ 9=a(-4)^2\implies 9=16a\implies \cfrac{9}{16}=a\qquad thus\quad \boxed{y=\cfrac{9}{16}(x-5)-3}[/tex]

The equation of the parabola with vertex (5, -3) and passing through (6, 1) in vertex form is y = [tex]4(x - 5)^2 - 3.[/tex]

To write the equation of a parabola in vertex form, we use the formula:

y = [tex]a(x - h)^2 + k[/tex]

where (h, k) is the vertex of the parabola. Given the vertex (5, -3) and a point (6, 1) the parabola passes through, we can plug these values into the equation to find a.

For the point (6, 1):

[tex]1 = a(6 - 5)^2 - 3[/tex]

[tex]1 = a(1)^2 - 3[/tex]

4 = a

So, the equation of the parabola in vertex form is:

y = [tex]4(x - 5)^2 - 3[/tex]

scuba diver is swimming 30 feet below sea level . A hand glider passes over the position of the scuba diver. The hand glider is 215 ft above sea level.
draw a number line to represent the distance between the scuba diver and the hand glider (include sea level at zero feet)

Answers

Attached the solution and work.

F(x, y) = y3/x, p(1, 3), u = 1 3 2i + 5 j (a) find the gradient of f.

Answers

Gabriella, it is important that you use "^" to denote exponentiation. "y3" doesn't cut it.

The gradient of F is (partial derivative of F with respect to x) i + (partial with respect to y) j.

Thus, G(x,y) = the gradient in question = (-y^3/x^2) i + (0) j (answer)

What is the interquartile range of 4 5 7 9 10 14 16 24

Answers

2's and 3's of GCF

HOpe iT hElpeED I'M cOOl

Answer:

The answer is 9

Step-by-step explanation: ? i did the the tetst or whatever and 9 is the correct answer.

YOUR WELCOME :}

The average American consumes about 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will 50 Americans consume in one week? Round to the nearest hundredth.

Answers

1 year has around 52.1429 weeks
We are given that one American consumes around 20 gallons of ice cream in a year. This means that the consumption is 20 gallons in 52.1429 weeks.
Now, first we will calculate the amount consumed by 1 American in one week using cross multiplication as follows:
consumption per week = (1*20) / (52.1429) = 0.38356 gallons

Now, to know the consumption of 50 Americans in one week, we will simply multiply the consumption of one American by 50 as follows:
consumption of 50 Americans = 0.38356 * 50 = 19.18 gallons/week

Jason bought 5 movie tickets and a bag of popcorn Jeremy bought 2 movie tickets they spent 54$ total. If the popcorn cost 5$, how much did each movie ticket cost?

Answers

total tickets: 7
Popcorn costs: $5
total cost: $54

7x + 5 = 54
- 5 -5

7x = 49

49/7 = 7

Final Answer: x=7

Without graphing, tell which statements are true for the graph of the function y = x2 + 2.

I. All points on the graph are above the origin.

II. All points on the graph have positive x-values.

III. All points on the graph have positive y-values.

Statements (... and ...) are true. Statement (...) is true because x^2 is non-negative for all values of x, so the minimum value of x^2 is 0. Thus, the minimum y−value for the function is (...) and the lowest point on the graph is (0, ...), which is above the origin. Statement (...) is true because the lowest point on the graph is (0, ...) so all other points have a y−value that is greater than (...) and must be positive.

Answers

The answers are choices one and three. Hope this helps!

Final answer:

Statements I and III are true as per the defined function y=x^2+2. The graph of this function would have all points above the origin and all points would have positive y-values. Statement II is incorrect as x can take both negative and positive values.

Explanation:

Considering the three statements given, only the statements I and III are true. This is because for the function y = x^2 + 2, all points on the graph are above the origin and all points on the graph have positive y-values.

Statement I is true because the function x^2 is non-negative for all values of x, which means that the minimum value of x^2 is 0. As a result, the minimum y−value for the function is 2 when x=0 and the lowest point on the graph is (0, 2), which is indeed above the origin.

Statement III is true because the lowest point on the graph is (0, 2) and since 2 is positive all other points have a y−value that is greater than 2 and therefore must be positive. Statement II is not true as x can take both negative and positive values in the function y=x^2+2.

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what is -8 3/4 + -11 1/3

Answers

The answer to this is -29/3, or -9.6...

Hope this helped!! ☺♥

The answer is -20 1/12.

Hope this helps! :D

~PutarPotato

PLZ HELP!!!!! D: D: IM FAILING PLZ HELP ;cccc

Answers

-2 is larger than -5
or
-2 is greater than -5

-----------------------------------------------------------------------------------------------------------

a loss of 5 points is greater in magnitude than a loss of 2 points
meaning that the person who lost 5 points had a bigger loss (even though -5 is smaller than -2)

Another way to think of it: -5 is further away from 0, compared to the distance from -2 to 0. I recommend drawing a number line if you're having trouble visualizing it.

When hired at a new job selling jewelry, you are given two pay options:

Option A: Base salary of $16,000 a year, with a commission of 7% of your sales

Option B: Base salary of $25,000 a year, with a commission of 2% of your sales

In order for option A to produce a larger income, you would need sell at least $_______ of jewelry each year

Answers

16,000 + 0.07x > 25,000 + 0.02x
0.07x - 0.02x > 25,000 - 16,000
0.05x > 9000
x > 9000 / 0.05
x > 180,000....so they would need to sell at least 180,001

You are required to sell a minimum of 180,001 of jewelry each year.

Given that,

The base salary is $16,000 per year and there is a 7% commission on sales for option A. The base salary is $25,000 per year and there is a 2% commission on sales for option B.Also, let us assume the sales be x

Based on the above information, the following expression should be made:

16,000 + 0.07x > 25,000 + 0.02x

0.07x - 0.02x > 25,000 - 16,000

0.05x > 9000

x > 9000 ÷ 0.05

x > 180,000

Therefore we can conclude that you are required to sell a minimum of 180,001 of jewelry each year.

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The median for the given set of 6 ordered data values is 32.5.
9, 12, 25, _, 41, 48
What is the missing value?

Answers

Being that u have a set of data that has an even number of numbers, the median (middle number) would be found by adding the 2 middle numbers and dividing by 2.

ur 2 middle numbers would be 25 and x...and when added, u divide by 2, u will get 32.5...so lets set it up as an equation.

(25 + x) / 2 = 32.5...multiply both sides by 2
25 + x = 32.5 * 2
25 + x = 65
x = 65 - 25
x = 40 <== ur missing number

Order these numbers from least to greatest. 14325 , 5.753 , 534 , 5.34

Answers

5.34, 5.753, 534, 14325

A rectangular floor is 24 feet long and 9 feet wide. What is the area of the floor in square yards?

Answers

The area of the floor in square yards is 24 yd.

if you multiply you should get 216.
24
x
9
_____
216

what is the decimal of 77/200?

Answers

0.385 is the decimal

0.385 is the decimal. Use a calculator and divide the numerator by the denominator

Is it possible to construct a triangle with side lengths of 11 cm, 15 cm, and 21 cm? Why or why not?

Answers

Assume the triangle is ABC with: AB = 11 ; AC = 15 and BC = 21.
To get a triangle each side should smaller than the addition of the other sides:

AB< AC+BC (11< 15+21) For this side it's ok
AC< AB+BC (15< 11+21) For this side it's ok
BC< AB+AC ( 21<11+15. This is wrong since 26=26 thus you can't draw a triangle with such measurements

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