Free Printable Modelling and Solving Exponentials

1.

Which of the following is an exponential decay model?

a)

$y=3000\left(-2\right)^x$

b)

$y=2\left(1.04\right)^x$

c)

$y=-\frac{3}{2}x-7$

d)

$y=40\left(0.79\right)^x$

2.

Consider the exponential growth equation $y=5678\left(1.60\right)^x$

What is the initial value?

(a)

3.

What is the correct multiplier (base) for an exponential model with a 45% rate of growth?

a)

1.45

b)

0.45

c)

1.045

d)

45

4.

What is the correct multiplier (base) for an exponential model that decreases at a rate of 5%?

a)

-0.05

b)

0.05

c)

0.95

d)

-5

5.

Choose the correct model:

Jo invests $500 in an account that earns 1.17% interest annually.

a)

$y=500\left(1.17\right)^x$

b)

$y=1.17\left(500\right)^x$

c)

$y=500\left(x\right)^{1.17}$

d)

$y=500\left(1.0117\right)^x$

6.

Choose the correct equation to solve:

There are initially 12 bacteria in a petri dish. The number of bacteria double every hour. How many bacteria would there be after 10 days?

a)

$y=12\left(2\right)^{10}$

b)

$y=12\left(2\right)^{240}$

c)

$y=12\left(10\right)^2$

d)

$y=2\left(12\right)^{240}$

7.

Choose the correct model to represent the value of an iPhone purchased in 2012:

A new iPhone cost $599 in 2012. It loses 34% of its value each year after 2012.

a)

$y=599\left(0.66\right)^x$

b)

$y=599\left(0.34\right)^{2012}$

c)

$y=599\left(1.34\right)^x$

d)

$y=2012\left(5.99\right)^{34}$

8.

Which of the following is an increasing exponential function whose y-intercept is 50?

a)

y = 50(.05)^x

b)

y = 50x - 4

c)

y = (2)^x + 50

d)

y = 50(1.4)^x

9.

A car tire fully inflated is losing 2.5% of its air everyday. The tire originally contained 4500 cubic inches of air. Which equation could be used to represent the loss of air

a)

$A=4500\left(1+2.5\right)^t$

b)

$A=4500\left(1+0.025\right)^t$

c)

$A=4500\left(1-0.025\right)^t$

d)

$A=4500\left(1-2.5\right)^t$

10.

Which graph below matches the function: f(x) = (1/3)^x

a)

b)

c)

d)

11.

What is the domain and range of the function y=2^x?
Use the graph to help!

a)

Domain: −∞<x<∞
Range: y>0

b)

Domain: −∞<x<∞
Range: y>1

c)

Domain: −2<x<∞
Range: y>0

d)

Domain: −∞<x<∞
Range: y>0

12.

Find an exponential model for the given table of values.

a)

$y=10\left(2\right)^x$

b)

$y=2\left(10\right)^x$

c)

$y=5\left(2\right)^x$

d)

$y=10\left(\frac{1}{2}\right)^x$

13.

Determine the RANGE of the exponential function.

a)

y > -8

b)

All Real Numbers

c)

y < -8

d)

y < 1

14.

Determine the ASYMPTOTE for the graph shown.

a)

y = 2

b)

y = -2

c)

x = -2

d)

x = 2

15.

Solve for x:
(-3)^x = (-3)¹³

a)

13

b)

-3

c)

x + 13

d)

x -13

16.

Solve for x using the same base method.
3^x-20= 27

a)

17

b)

27

c)

-7

d)

23

17.

Solve the exponential equation:

a)

-11/4

b)

6

c)

9/4

d)

8

18.

Rewrite in logarithmic form:

6² = 36

a)

log₆ 2 = 36

b)

log₆ 36 = 2

c)

ln 36 = 2

d)

6³⁶ = 2

19.

Rewrite in exponential form:

log₃(9)=2.

a)

3⁹=2

b)

3²=9

c)

x²=9

d)

3^x=2

20.

Solve the equation for x

(Tech Active Question)

a)

x = 2

b)

x = 3

c)

x = 8

d)

x = 64

21.

Solve x in this Tech-Active Question:

7^x = 36

a)

1.8416

b)

3.5835

c)

1.5563

d)

3.0903

22.

Solve for x in this Tech Active Question:

5(4)^x-2 - 29 = 6

a)

-.5609

b)

3.4036

c)

2.0674

d)

-1.0753

Modelling and Solving Exponentials

Total questions: 22

Worksheet time: 56mins

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