Math: Unit Test

The table represents an exponential function. What is the multiplicative rate of change of the function?

1/5

Lena is asked to write an explicit formula for the graphed geometric sequence. What value, written as a decimal, should Lena use as the common ratio?

2.5

What is the multiplicative rate of change of the function shown on the graph? Express your answer in decimal form. Round to the nearest tenth.

2.5

Consider the graph of the exponential function in the form of f(x) = a(bx). The value of a in the function is

3

What is the initial value of the exponential function shown on the graph?

4

Which value of a in the exponential function below would cause the function to shrink? f(x) = a(3/2)x

4/5

-2 0.004 -1 0.02 0 0.1 1 0.5 What is the growth factor of the exponential function represented by the table?

5

What is the multiplicative rate of change of the function described in the table?

5

Ramon is graphing the function f(x) = 3(4)x. He begins by plotting the initial value. Which graph represents his initial step?

A.

Which is the graph of f(x) = 2(3)x?

A.

Which is the graph of f(x) = 5(2)x?

A.

Which is the graph of the sequence defined by the function f(x + 1) = 3/5 f(x) when the first term in the sequence is 375?

A.

The graph of f(x) = 2x is shown on the grid. The graph of g(x) = ()x is the graph of f(x) = 2x reflected over the y-axis. Which graph represents g(x)?

B.

Which graph represents a function with an initial value of 1/2?

B.

Which graph represents a geometric sequence?

B.

Which graph shows exponential growth?

B.

Which is the graph of f(x) = 3/2(1/3)x?

B.

The table represents an exponential function. What is the multiplicative rate of change of the function?

B. 2/3

Chelsea is graphing the function f(x) = 20()x. She begins by plotting the initial value. Which graph represents her first step?

C.

Which graph represents exponential decay?

C.

Which function could be a stretch of the exponential decay function shown on the graph?

C. f(x) = 2(1/6)x

Which exponential function is represented by the graph?

C. f(x) = 3(2x)

Which is the graph of the sequence defined by the function f(x + 1) = 2/3f(x) if the initial value of the sequence is 108?

D.

Which explains why the graphs of geometric sequences are a series of unconnected points rather than a smooth curve?

The domain contains only natural numbers.

What are the domain and range of the function on the graph?

The domain includes all real numbers, and the range is y > 0.

Keshawn is asked to compare and contrast the domain and range for the two functions. f(x) = 5x g(x) = 5x Which statements could he include in his explanation? Check all that apply.

The domain of both functions is all real numbers. The range of g(x) is y > 0.

640, 160, 40, 10, ... Which correctly describe the graph of the geometric sequence? Check all that apply.

The domain will be the set of natural numbers. The graph will show exponential decay.

Pablo generates the function to determine the xth number in a sequence. Which is an equivalent representation?

f(x + 1) = 5/2f(x)

-2 12.5 -1 2.5 ... Which exponential function is represented by the table?

f(x) = 0.5(0.2x)

-2 0.2 -1 0.4 0. 0.8 ... Which exponential function is represented by the table?

f(x) = 0.8(2x)

1.2, 3, 7.5, 18.75, ... Which formula can be used to describe the sequence?

f(x) = 1.2(2.5)x - 1

Which is a shrink of an exponential growth function?

f(x) = 1/3(3)x

Which formula can be used to describe the sequence? -2/3, −4, −24, −144,...

f(x) = 2/3(6)x − 1

Sebastian writes the recursive formula f(x+1) = 4f(x) to represent a geometric sequence whose second term is 12. Which explicit formula can be used to model the same sequence?

f(x) = 3(4)x − 1

Which is a stretch of an exponential growth function?

f(x) = 3/2(3/2)x

Which is an exponential decay function?

f(x) = 3/2(8/7)-x

Which function represents exponential growth?

f(x) = 3x

Which function represents exponential decay?

f(x) = 4(2/3)x

Which equation represents an exponential function with an initial value of 500?

f(x) = 500(2)x

Which formula can be used to describe the sequence? -3, 3/5, -3/25, 3/125, -3/625

f(x) = −3(1/5)x-1

Consider the exponential function f(x) = 1/5(15x). What is the value of the growth factor of the function?

D. 15

-1 18 0 6 ... What is the decay factor of the exponential function represented by the table?

1/3

Which is the initial value that shrinks an exponential growth function by 50%?

1/2

Pherris is graphing the function f(x) = 2(3)x. He begins with the point (1, 6). Which could be the next point on his graph?

(2, 18)

Tanisha is graphing the function f(x) = 25(3/5)x. She begins by plotting the point (1, 15). Which could be the next point she plots on the graph?

(2, 9)

The function f(x) = 5()x is reflected over the y-axis. Which equations represent the reflected function? Check all that apply.

(x) = 5(1/5)-x f(x) = 5(5)x

What is the multiplicative rate of change for the exponential function f(x) = 2()-x?

0.4

The curve through the ordered pairs (0, 10), (1, 5), and (2, 2.5) can be represented by the function f(x) = 10(0.5)x. What is the multiplicative rate of change of the function?

0.5

The table represents an exponential function. What is the multiplicative rate of change of the function?

0.5

Hal is asked to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually. What multiplicative rate of change should Hal use in his function?

0.98

A conservationist determines that a particular beach is eroding at a rate of 1.1% each year. When writing an explicit formula to represent the amount of beach remaining each year, which value should she use as the common ratio?

0.989

Natalia is writing a recursive formula to represent the sequence. 8, 12, 18, 27, ... What value should she use as the common ratio in the formula? Write the answer as a decimal rounded to the tenths place.

1.5

A limited-edition poster increases in value each year. After 1 year, the poster is worth $20.70. After 2 years, it is worth $23.81. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.)

y = 18(1.15)x

The value of a collector's item is expected to increase exponentially each year. The item is purchased for $500. After 2 years, the item is worth $551.25. Which equation represents y, the value of the item after x years?

y = 500(1.05)x

After 1 year, a bank account contains $7,746.90. After 2 years, the same account contains $7,901.84. Assuming no deposits or withdrawals are made, which equation can be used to find y, the amount of money in the account after x years? (Round money values to the nearest penny.)

y = 7595(1.02)x