Unit 6 Intervention Practice Test

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Formulas

Exponential function:   f(x)=a(b)^x

Exponential GROWTH Function:    y=a(1+r)^t

Exponential DECAY Function:    y=a(1-r)^t

Which exponential function matches the values in the table below?

f(x)=64(2)^x

f(x)=1(8)^x

f(x)=x^8

f(x)=8x

What are the next three terms in the sequence 20, 10, 5, 2.5, ...?

1.5, 0.5, -1.5

2, 1.5, 1

1.25, 0.625, 0.3125

When a ball is dropped, the function f(x) =4(0.6)^x models the ball’s height in feet after each bounce, where x is the bounce number. To the nearest hundredth, what is the height after the third bounce?

0.86 feet

8.64 feet

7.20 feet

1.80 feet

The first term of a geometric sequence is 8 and the common ratio is 3. What is the fifth term of the sequence?

1944

120

512

648

Evaluate y=4(2)^x when x=3

What is the value of x?

The population of a town over the past 10 years can be represented with the equation y =2450(1.07)^x.
Which statement below is FALSE?

At the end of the first year, the population was 2450.

The initial population had a growth rate of 7%.

At the end of the third year, the population was approximately 3000.

The initial population was 2450.

Which set of ordered pairs satisfies an exponential equation?

{(1, -2), (3, 2), (5, 6), (7, 10)}

{(1, 1), (2, 8), (3, 27), (4, 64)}

{(1, -1), (2, -4), (3, -9), (4, -16)}

{(1, 2), (3, 8), (5, 32), (7, 128)}

Select ALL expressions that equal 4 when simplified.

Complete the table and graph the function.
Click "show your work".

Does this function represent growth or decay?

growth

decay

Select the correct Domain and Range for the graph below.

Select TWO:

A pond has 130 fish, and the population decreases by 8% each day. Find the number of fish in the pond after 4 days.

Round to the nearest whole number.

Ira has $100 in his savings account. He is looking at two savings plans.

Under Plan A, his account balance can be represented with the equation f(t)=100+10t each year.

Under Plan B, his account balance can be represented with the equation g(t)=100(1.09)^t each year.

Complete the table then select the THREE statements that are TRUE.

Plan B has a bigger balance after 2 years

After 1 year both plans have the same balance

Plan B shows exponential growth

Plan A has a bigger balance for the first 3 years

Ira should invest in Plan B if he plans to leave his money in the account for 4 years or more.

The balance for Plan A will always be greater than Plan B

Describe the end behavior for the function:

A scientist tracked the population of northern sea otters from 2015 to 2020. In 2015 there were 70 sea otters. According to the scientist, the population was increasing at a rate of 18% annually.

Write the function P(t) that describes the population of sea otters as a function of the number of years, t.

Which exponential function matches the values in the table below?

f(x)=64(2)^x

f(x)=1(8)^x

f(x)=x^8

f(x)=8x

What are the next three terms in the sequence  20, 10, 5, 2.5, ...?

1.5, 0.5, -1.5

2, 1.5, 1

1.25, 0.625, 0.3125

When a ball is dropped, the function f(x) =4(0.6)^x models the ball’s height in feet after each bounce, where x is the bounce number. To the nearest hundredth, what is the height after the third bounce?

0.86 feet

8.64 feet

7.20 feet

1.80 feet

The first term of a geometric sequence is 8 and the common ratio is 3. What is the fifth term of the sequence?

1944

120

512

648

The population of a town over the past 10 years can be represented with the equation  y =2450(1.07)^x. 
Which statement below is FALSE?

At the end of the first year, the population was 2450.

The initial population had a growth rate of 7%.

At the end of the third year, the population was approximately 3000.

The initial population was 2450.

Which set of ordered pairs satisfies an exponential equation?

{(1, -2), (3, 2), (5, 6), (7, 10)}

{(1, 1), (2, 8), (3, 27), (4, 64)}

{(1, -1), (2, -4), (3, -9), (4, -16)}

{(1, 2), (3, 8), (5, 32), (7, 128)}

Select ALL expressions that equal 4 when simplified.

Does this function represent growth or decay?

growth

decay

Select the correct Domain and Range for the graph below.

Select TWO:

Range: all real numbers

Range: y>0

Domain:  x>-13

Domain:  all real numbers

Domain:  x>0

Range: y>-3

Ira has $100 in his savings account. He is looking at two savings plans. 

Under Plan A, his account balance can be represented with the equation  f(t)=100+10t each year. 

Under Plan B, his account balance can be represented with the equation g(t)=100(1.09)^t each year.

Complete the table then select the THREE statements that are TRUE.

Plan B has a bigger balance after 2 years

After 1 year both plans have the same balance

Plan B shows exponential growth

Plan A has a bigger balance for the first 3 years

Ira should invest in Plan B if he plans to leave his money in the account for 4 years or more.

The balance for Plan A will always be greater than Plan B

Describe the end behavior for the function: 

Unit 6 Intervention Practice Test

Unit 6 Intervention Practice Test

Evaluate y=4(2)^x when x=3

What is the value of x?

Complete the table and graph the function. Click "show your work".

A pond has 130 fish, and the population decreases by 8% each day. Find the number of fish in the pond after 4 days.Round to the nearest whole number.

Which exponential function matches the values in the table below?

What are the next three terms in the sequence 20, 10, 5, 2.5, ...?

When a ball is dropped, the function f(x) =4(0.6)^x models the ball’s height in feet after each bounce, where x is the bounce number. To the nearest hundredth, what is the height after the third bounce?

The first term of a geometric sequence is 8 and the common ratio is 3. What is the fifth term of the sequence?

Evaluate y=4(2)^x when x=3

What is the value of x?

The population of a town over the past 10 years can be represented with the equation y =2450(1.07)^x. Which statement below is FALSE?

Which set of ordered pairs satisfies an exponential equation?

Select ALL expressions that equal 4 when simplified.

Complete the table and graph the function. Click "show your work".

Does this function represent growth or decay?

Select the correct Domain and Range for the graph below.Select TWO:

A pond has 130 fish, and the population decreases by 8% each day. Find the number of fish in the pond after 4 days.Round to the nearest whole number.

Describe the end behavior for the function:

Complete the table and graph the function.
Click "show your work".

A pond has 130 fish, and the population decreases by 8% each day. Find the number of fish in the pond after 4 days.

Round to the nearest whole number.

The population of a town over the past 10 years can be represented with the equation y =2450(1.07)^x.
Which statement below is FALSE?

Complete the table and graph the function.
Click "show your work".

Select the correct Domain and Range for the graph below.

Select TWO:

A pond has 130 fish, and the population decreases by 8% each day. Find the number of fish in the pond after 4 days.

Round to the nearest whole number.