Free Printable exponential growth and decay

1.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

2.

What type of function is y = 7(5/4)^x?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

3.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

4.

What is a, the initial amount, for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

5.

A 78 gram sample of Uranium loses half of its mass each year. What is the exponential equation?

a)

y=78(0.5)^x

b)

y=78(1.5)^x

c)

y=78(2)^x

6.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

7.

Is this exponential growth or decay?

a)

Growth

b)

Decay

c)

Linear

8.

What does the a in y=a(1+r)^x represent?

a)

Time

b)

Rate

c)

Slope

d)

Initial Amount

9.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

10.

What type of function is f(x)=2(1/7)^x ?

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

d)

None of the Abovee

11.

What is the decay rate in the following model?

A=1200(.85)⁶

a)

1200

b)

.15

c)

.85

d)

6

12.

What is the decay factor in the following model?
A=1200(.85)⁶

a)

1200

b)

-.15

c)

.85

d)

A

13.

What is r, the growth rate, for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

14.

Is y = 5(1.04)^x growth or decay?

a)

Growth

b)

Decay

15.

Is y = 4(.20)^x growth or decay?

a)

Growth

b)

Decay

16.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

17.

Is the pictured graph growth, decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

18.

Is this exponential growth or decay?

a)

Growth

b)

Decay

19.

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

a)

14327

b)

4309

c)

839

d)

7680

20.

A stamp gets more expensive each year. It increases in value by 60 % each year. What is the growth FACTOR?

a)

.6

b)

1.06

c)

1.6

d)

.4

21.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

22.

What is the pattern you see in this table?

a)

Common Ratio = 1/3

b)

Common Difference = 8

c)

Common Ratio = 3

d)

Common difference = 3

23.

Which equation matches the graph?

a)

y=2(2)^x

b)

y=2(1/2)^x

c)

y=2^x

d)

y=1/2(2)^x

24.

What is the equation that represents the exponential function in the image below?

a)

y=3(½)^x

b)

y=3(2)^x

c)

y=(2)^x

d)

y=2(3)^x

25.

A population of 1500 deer decreases by 1.5% per year. At the end of 10 years, there will be approximately 1290 deer in the population.

Which function can be used to determine the number of deer, y, in this population at the end of t years?

a)

$y=1500(1-0.015)^t$

b)

$y=1500(0.015)^t$

c)

$y=1500(1+0.015)^t$

d)

$y=1500(1.5)^t$

26.

There were 417 cell phones sold at an electronics store in January. Since then, cell phone sales at this store have increased at a rate of 3.75% per month.

At this rate of growth, which function can be used to determine the monthly cell phone sales x months after January?

a)

$f(x)=417(1-0.0375)^x$

b)

$f(x)=417(1-3.75)^x$

c)

$f(x)=417(1+0.0375)^x$

d)

$f(x)=417(1+3.75)^x$

27.

Classify the model as Exponential GROWTH or DECAY.

$A=10(1.01)^3$

a)

Growth $y=a\left(1+r\right)^t$

b)

Decay $y=a\left(1-r\right)^t$

28.

A population of fish starts at 8,000 and increases by 6% per year.

What will the fish population be in 10 years?

a)

$14,327$

b)

$4309$

c)

$839$

d)

$7680$

29.

This is an example of:

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

30.

This is an example of:

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

31.

This is an example of: $f\left(x\right)=\ 25\ \left(\ 0.20\right)^x$

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

32.

How do you know that this was exponential growth? $f\left(x\right)=0\ .25\ \left(\ 1.3\right)^x$

a)

Because the 0.25 was bigger than one

b)

Because the 1.3 was bigger than one

c)

Because the 0.25 was less than one

d)

Because the 1.3 was less than one

33.

This is an example of: $f\left(x\right)=3\ \left(\ \frac{5}{2}\right)^x$

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

34.

How do we know that is an example of an exponential decay?

a)

Its a line going up

b)

Its a line going down

c)

Its a smooth curve going down

d)

Its a smooth curve going up

35.

In an exponential function, what does the 'a' represent?

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

36.

If f(x) = 2x-9, what is f(3)?

a)

6

b)

-3

c)

3

d)

-6

37.

A population of 2200 beetles is too large to sustain and decreases in population each month at a rate of 5%. How would you write your growth rate, b?

a)

-5

b)

-.05

c)

.95

d)

.05

38.

A bicycle depreciates at a rate of 15%. Therese bought a bicycle for $250. IS this an example of an exponential function?

a)

yes, exponential growth

b)

yes, exponential decay

c)

None

39.

Describe the function:
y = 57(1/3)^x

a)

growth by factor of 1/3

b)

decay by factor of 1/3

c)

growth by 2/3

d)

decay by 1/3 %

40.

Give the rate of decay:
y = 35(0.65)^x

a)

35%

b)

65%

c)

.35%

d)

165%

41.

Describe the function:
y = 1000(1 - 0.87)^x

a)

growth by 87%

b)

decay by 87%

c)

growth by 13%

d)

decay by 13%

42.

Determine the y-intercept of the function:
y = 1.25(5)^x

a)

5

b)

1

c)

.25

d)

1.25

43.

The population of turtles is doubling every 6 months. If there are 400 turtles now, how many will there be in 2 years? (Choose equation)

a)

y = 400(2)²

b)

y = 400(2)⁶

c)

y = 400(2)⁴

d)

y = 400 + 2(8)

44.

The growth factor for this table is

a)

2

b)

4

c)

12

d)

144

45.

The equation for this table is

a)

y = 3x + 50

b)

y = 50^x

c)

y = 3^x

d)

y = 50(3^x)

46.

The equation for this table is

a)

y = 1(2^x)

b)

y = 1(12^x)

c)

y = 12x

d)

y = 12x + 1

47.

Is the Equation Linear or Exponential?

a)

Linear

b)

Exponential

48.

Is the Equation Linear or Exponential?

a)

Linear

b)

Exponential

49.

Is the Equation Linear or Exponential?

a)

Linear

b)

Exponential

50.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

exponential growth and decay

Total questions: 50

Worksheet time: 2hrs 0mins

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