Does each function describe exponential growth or decay?
Drag and drop the equations into the boxes to correctly complete the table.
Growth Decay
y=100(1−12)^t
y=0.1(1.25)^t
y=((1−0.03)12)^2t
y=426(0.98)^t
y=2050(12)^t
Answers
A function [tex]f[/tex] from a set [tex]A[/tex] to a set [tex]B[/tex] is a relation that assigns to each element [tex]x[/tex] in the set [tex]A[/tex] exactly one element [tex]y[/tex] in the set [tex]B[/tex]. The set [tex]A[/tex] is the domain (also called the set of inputs) of the function and the set [tex]B[/tex] contains the range (also called the set of outputs).
[tex]We \ denote \ the \ \mathbf{exponential \ function} \ f \ with \ base \ a \ as: \\ \\ f(x)=a^x \\ \\ where \ a>0, \ a\neq 1, \ and \ x \ is \ any \ real \ number[/tex].
1. It isn't an exponential function.
We have the following equation:
[tex]y=100(1-12)^t[/tex]
That can be written as:
[tex]y=100(-11)^t[/tex]
Recall that the definition of exponential functions establishes that:
[tex]We \ denote \ the \ \mathbf{exponential \ function} \ f \ with \ base \ a \ as: \\ \\ f(x)=a^x \\ \\ where \ a>0, \ a\neq 1, \ and \ x \ is \ any \ real \ number[/tex].
That is:
[tex]a \ \mathbf{must} \ be \ greater \ than \ 1[/tex]
In this problem, [tex]a=-11[/tex], therefore this is not an exponential function.
2. Growth.
The function:
[tex]y=0.1(1.25)^t[/tex]
is an exponential function because is a function of the form [tex]f(t)=ka^t \\ \\ where \ a>0 \ and \ k \ constant[/tex]
So [tex]k=0.1 \ and \ a=1.25[/tex]. Since [tex]a \ is \ greater \ than \ 1[/tex] and being raised to the power of [tex]t[/tex], the function increases. This means that [tex]y[/tex] increases as [tex]t[/tex] increases as illustrated in Figure 1. This represents a growth.
3. Growth.
The function:
[tex]y=((1-0.03)12)^{2t}[/tex] can be written as:
[tex]y=11.64^{2t}[/tex]
and is an exponential function because is a function of the form [tex]f(t)=a^{bt} \\ \\ where \ a>0 \ and \ b \ constant[/tex]
So [tex]a=11.64 \ and \ b=2[/tex]. Since [tex]a \ is \ greater \ than \ 1[/tex] and being raised to the power of [tex]2t[/tex], the function increases. As in the previous exercise, this means that [tex]y[/tex] increases as [tex]t[/tex] increases as illustrated in Figure 2. This represents a growth.
4. Decay.
The function:
[tex]y=426(0.98)^t[/tex]
is an exponential function because is a function of the form [tex]f(t)=ka^t \\ \\ where \ a>0 \ and \ k \ constant[/tex]
So [tex]k=426 \ and \ a=0.98[/tex]. Since [tex]a \ is \ less \ than \ 1[/tex] and being raised to the power of [tex]t[/tex], the function decreases. Here this means that [tex]y[/tex] decreases as [tex]t[/tex] increases as illustrated in Figure 3. This represents a decay.
5. Growth.
The function:
[tex]y=2050(12)^t[/tex]
is an exponential function because is a function of the form [tex]f(t)=ka^t \\ \\ where \ a>0 \ and \ k \ constant[/tex]
So [tex]k=2050 \ and \ a=12[/tex]. Since [tex]a \ is \ greater \ than \ 1[/tex] and being raised to the power of [tex]t[/tex], the function increases. So in this function [tex]y[/tex] also increases as [tex]t[/tex] increases as illustrated in Figure 4. This represents a growth.
Answer:
1. isn't an exponential function
2. growths
3. growths
4. decay
5. growths
Step-by-step explanation:
The exponential functions has the form: y = k1*k2^(k3*t), where k1, k2 and k3 are a constants, and k2>0. Graph of exponential functions always decrease or always increase. To know if a function growths or decay just evaluate the function in 2 points, for example t = 0 and t = 1, and compare their results.
1.
y = 100*(1−12)^x = 100*(−11)^x
Since (-11) is negative, then y is not an exponential function
2.
y(0) = 0.1*(1.25)^(0) = 0.1
y(1) = 0.1*(1.25)^(1) = 0.125
y(1) > y(0) -> growths
3.
y(0) =((1−0.03)12)^2(0) = 1
y(0) =((1−0.03)12)^2(1) = 135.4896
y(1) > y(0) -> growths
4.
y(0) = 426(0.98)^(0) = 426
y(1) = 426(0.98)^(1) = 417.48
y(1) < y(0) -> decay
5.
y(0) = 2050(12)^(0) = 2050
y(1) = 2050(12)^(1) = 24600
y(1) > y(0) -> growths
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Marcello is constructing the perpendicular bisector of AB¯¯¯¯¯. He has already constructed arcs as shown.
What should Marcello do for his next step?
A. Use the straightedge to draw AX←→ and AY←→.
B. Use the straightedge to draw a line through points X and Y.
C. Place the point of the compass on point X and draw an arc, using AX as the width for the opening of the compass.
D. Place the point of the compass on point X and draw an arc, using AY as the width for the opening of the compass.
Answers
The radius of the arc must be more than half the length of the line.
By drawing a line through the 2 intersections of the arcs, you will get the perpendicular of the line.
Answer is B.
The sum of two numbers is 35 . the smaller number is 19 less than the larger number. what are the numbers?
Answers
x+x+19=35
2x=16
x=8
x+19=27
the numbers are 8 and 27.
6a - 10 = 3a + 17 please explain how you got your answer
Answers
next we add 3a + 17 + 10 so it can be 3a + 27
next we subtract 3a from both sides
next we subtract 6a - 3a and we get 3a
then we divide both sides by 3
and lastly we divide 27/3 to get our answer
Answer: a = 9.
Tape diagram to subtract 33-19
Answers
To subtract 19 from 33 using a tape diagram, draw a rectangle labeled 33, mark off a section labeled 19, and the unshaded difference represents the result, which is 14.
To create a tape diagram to show the subtraction of 33-19, we start by drawing a long rectangle to represent the number 33. We then mark off the length that represents the number 19 on the same tape, indicating the part we want to subtract. Lastly, the remaining part of the tape diagram represents the difference between the two numbers.
Draw a rectangle and label it 33.Mark a section of the rectangle and label it 19.Shade in or distinguish the remaining part of the rectangle; this is the result of 33 minus 19.See the unshaded part, which represents the difference, and count if necessary to find that it equals 14.The final result is the length of the unshaded part of the tape diagram, which shows the difference when you subtract 19 from 33.
Mark the statements that are true.
A. An angle that measures is a reflex angle.
B. An angle that measures 65 is an acute angle.
C. An acute angle measures less than .
D. An angle that measures 300 is an obtuse angle.
Answers
The correct options are B. An angle that measures 65 is an acute angle. and C. An acute angle measures less than 90 degrees.
To determine the truth of each statement, let's analyze each option:
A. An angle that measures 180 degrees is a reflex angle.
This statement is false. An angle that measures exactly 180 degrees is a straight angle, not a reflex angle. A reflex angle is greater than 180 degrees but less than 360 degrees.
B. An angle that measures 65 degrees is an acute angle.
This statement is true. An acute angle is an angle that measures less than 90 degrees. Since 65 degrees is less than 90 degrees, it is indeed an acute angle.
C. An acute angle measures less than 90 degrees.
This statement is true. By definition, an acute angle is any angle whose measure is less than 90 degrees.
D. An angle that measures 300 degrees is an obtuse angle.
This statement is false. An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. Since 300 degrees is greater than 180 degrees, it is not an obtuse angle but rather a reflex angle.
Which function below has the smallest slope?
f(x)
f(x) = 2x − 3
g(x)
graph going through (0, negative 5) and (4, 3)
h(x)
x h(x)
−1 3
1 7
3 11
f(x)
g(x)
h(x)
The functions all have the same slope
Answers
Answer: The functions all have the same slope
Step-by-step explanation:
just took the assessment and I got it right.
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Answers
Answer:
She is incorrect because 2.81 × 10^4 is around 30,000 so the units must be smaller than feet. She most likely measured in inches.
Help please
Solve for r.
s=2πrh
Answers
hope this helps u
I hope that will help you
y + 3 = –y + 9 solve
Answers
y + 3 = -y + 9
Add y to both sides.
2y + 3 = 9
Subtract 3 from both sides.
2y = 6
Then divide 2 to solve for y.
y = 6
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If chungs go kart can travel 48 miles on 1 gallon of gas,how far can his go kart travel with 1.15 gallons of gas?
Answers
you take 1.15 times 48
i hoped i helped
Set up a proportion. 1 over 48 is equal to 1.15 over x. Use cross products multiply 48 by 1.15 to get 55.2 and divide that by 1 to get 55.2.
x=55.2 miles.
Hope this helps!
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Hurry When solving a system of equations, Jared found y = x 10 for one equation and substituted x 10 for y in the other equation. Nicole found x = y – 10 for the same equation and substituted y – 10 for x in the other equation. Who is correct? Explain.
Answers
Jared and Nicole both have found the correct value and will get the same solution to the system of equations.
Given information:
Jared found that [tex]y = \dfrac{x} {10}[/tex] for one equation and substituted [tex]\dfrac{x}{10}[/tex] for y in the other equation.
Nicole found [tex]x = y -10[/tex] for the one equation and substituted [tex]y -10[/tex] for x in the other equation.
So, there are two equations. Based on the question, the equation should be,
[tex]x=10y[/tex] and [tex]y-x=10[/tex].
Now, Jared and Nicole have found the value of one variable from one equation and have put it in the other equation.
This method is the substitution method which is used to find the solution of the system of equations.
Therefore, Jared and Nicole both have found the correct value and will get the same solution to the system of equations.
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Terrance bought 3 markers. his sister bought 5 markers. terrance and his sister spent a total of $16 on the markers. what was the price of each marker?
Answers
If six plus two what does it equal
Answers
Two = 2
6 + 2 = 8
For a craft project, two equilateral triangles are taped together to create a quadrilateral
Answers
Find two consecutive integers whose sum is 67.
Which of the following equations could be used to solve the problem?
2x = 67
2x + 1 = 67
2x + 2 = 67
x2 + 1= 67
Answers
The next larger consecutive integer is 1 more than x, so it's x + 1.
x + x + 1 = 67
2x + 1 = 67
Answer is option B.
Answer:
2x + 1 = 67
Let the smaller integer be x.
The next larger consecutive integer is 1 more than x, so it's x + 1.
x + x + 1 = 67
2x + 1 = 67
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Look at a point on the graph, for example, (0, -4).
How much do you need to go up and then right to get to the next point?
If you go up 1 and right 1, you get to point (1, -3) which is also on the graph.
Going up 1 is a rise of 1.
Going right 1 is a run of 1.
Slope = rise/run = 1/1 = 1
The diameter of the circle above is 94 cm. what is the circumference of the circle? (use = 3.14.)
Answers
94 * 3.14 = 295.16
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He length of a rectangle is six times its width. if the perimeter of the rectangle is 70 in , find its area.
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Eli needs to save $235. to earn money, he plans to mow lawns and charge $21 for each, write two estimates eli could use to determine the number of lawns he needs to mow. decide which estimate you think is the better one for eli to use
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Find the lengths of the missing sides if side a is opposite angle a, side b is opposite angle b, and side c is the hypotenuse.
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Julie needs 3 lengths of string that are each 6 inches long. Marlene needs 7 lengths of string that are each 8 inches long.
How much string do the girls need altogether?
in.
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Which of these fractions can be written as a recurring decimal 1/2 1/3 1/4 1/5
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What is the measure of an angle if the measure of its supplement is 39 degrees more than twice the measure of its complement?
Answers
180-x = 2(90-x)+39
180-x = 180-2x+39
180-x = 219-2x
180+x = 219
x = 39
Measure of angle is equals to 39degrees as per given conditions of supplement and complement angles.
What is angle?" Angle is defined as when two rays meet at one endpoint known as vertex."
According to the question,
'x' represents the measure of an angle
Measure of its supplement angle = 180 - x
Measure of its complement angle= 90 - x
As per given condition of angle we get,
[tex]180 - x = 2(90 - x) +39\\\\\implies 180-x= 180 -2x +39\\\\\implies 2x-x = 39\\\\\implies x=39degrees[/tex]
Hence, measure of angle is equals to 39degrees as per given conditions of supplement and complement angles.
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A histogram can help you make predictions about a set of data. True False
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Which arrangement shows 26/4 , 6.45, 6 2/5 , and 50/8 in order from least to greatest?
{A} 6 2/5 , 50/8 , 6.45, 26/4
{B} 50/8 , 6 2/5 , 26/4 , 6.45
{C} 26/4 , 50/8 , 6 2/5 , 6.45
{D} 50/8 , 6 2/5 , 6.45, 26/4
Answers
Answer:
Option D) [tex]\displaystyle\frac{50}{8} < 6\frac{2}{5} < 6.45 < \frac{26}{4}[/tex]
Step-by-step explanation:
We are given the following information in the question:
We are given a set of numbers:
[tex]\displaystyle\frac{26}{4}, 6.45, 6\frac{2}{5}, \frac{50}{8}[/tex]
First, we write all the numbers in decimal form.
[tex]\displaystyle\frac{26}{4} = 6.5\\\\6\frac{2}{5} = \frac{32}{5} = 6.4\\\\\frac{50}{8} = 6.25[/tex]
Hence, the given numbers are:
6.5, 6,45, 6.4, 6.25
Arranging in order of least to greatest:
[tex]6.25 < 6.4 < 6.45 < 6.5[/tex]
Thus,
[tex]\displaystyle\frac{50}{8} < 6\frac{2}{5} < 6.45 < \frac{26}{4}[/tex]
Option D is the correct option.
Hot dogs cost $2.00 each, candy bars cost $1.00 each, and soft pretzels cost $2.50 each. How much would it cost to buy two hot dogs and one candy bar?
a. too much
b. too little
Answers
To calculate the total cost, multiply the price of each item by the number purchased then add those totals together. In this case, purchasing two hot dogs and one candy bar costs $5.00.
Explanation:To find the total cost of purchasing two hot dogs and one candy bar, you would simply multiply the cost of each item by the number of that item you are buying, and then add all these costs together. So, if a hot dog is $2.00 and you want to buy two, this costs $2.00 * 2 = $4.00. A candy bar is $1.00 each, and if you want to buy one, this costs $1.00 * 1 = $1.00. So, the total cost would be the cost of the hot dogs plus the cost of the candy bar, which is $4.00 + $1.00 = $5.00. Therefore, the total cost of two hot dogs and one candy bar is $5.00.
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For the given function, find the vertical and horizontal asymptote(s) (if there are any). f(x) = the quantity x squared plus three divided by the quantity x squared minus nine
Answers
__________________________________________
The horizontal asymptote is: "y = 2" .
___________________________________________
Explanation:
___________________________________________
f(x) = [tex] \frac{x^{2}+ 3}{ x^{2} - 9}[/tex] ;
We know that "(x² − 9) ≠ 0 ; since we cannot divide by "0" ; so the "denominator" in the fraction cannot be "0" ;
since: 9 − 9 = 0 ; "x² " cannot equal 9.
So, what values for "x" exist when "x = 9" ?
x² = 9 ;
Take the square root of EACH SIDE of the equation ; to isolate "x" on one side of the equation ; and to solve for "x" ;
√(x²) = √9 ;
x = ± 3
__________________________________________
So; the vertical asymptotes are: "x = 3" and "x = -3" .
__________________________________________
The horizontal asymptote is: "y = 2" .
__________________________________________
(since: We have: f(x) = [tex] \frac{x^{2}+ 3}{ x^{2} - 9}[/tex] ;
The "x² / x² " as the highest degree polymonials; both with "implied" coefficients of "1" ; and both raised to the same exponential power of "2".
what is the relationship between two lines that intersect to form angles?
Answers
A total of 820 tickets were sold for the school play. they were either adult tickets or student tickets. there were 70 more student tickets sold than adult tickets. how many adult tickets were sold?
Answers
By setting up a system of equations, we find that 375 adult tickets were sold for the school play.
To solve this problem, we need to set up a system of equations using the information provided:
There are only two types of tickets: adult tickets and student tickets.A total of 820 tickets were sold.There were 70 more student tickets sold than adult tickets.Let's define the following variables:
A for the number of adult tickets.S for the number of student tickets.According to the problem:
A + S = 820 (since the total number of tickets is 820)S = A + 70 (since there are 70 more student tickets than adult tickets)Now we substitute the second equation into the first:
A + (A + 70) = 8202A + 70 = 8202A = 750A = 375So, 375 adult tickets were sold.
HELP PLEASE ASAP!!!!!!!!!!!!!!!!!!!!
Answers
They added 5+16 but instead they should've divided 42/5.
Hope this was fast enough!