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Yui makes a list of the balances in her savings account at the end of each month. She notices that each month’s total is 5% greater than the previous month’s total. She writes a recursive formula to describe the account balances.

0.05

0.5

1.05

5.0

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The table represents an exponential function.

Two-thirds

Three-fourths

Four-thirds

Three-halves

Which table shows exponential decay?

A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 16, 8, 4, 2.

A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 16, 128, 8, 4.

A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 16, 12, 9, 7.

A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 16, 8, 3, 1.

The function f(x) = 2·5x can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the multiplicative rate of change of the function?

Which is the graph of f(x) = (4)x?

Option

1.2, 3, 7.5, 18.75, ...

f(x) = 1.2(2.5)x – 1

f(x) = 2.5(1.2)x – 1

f(x) = 1.2(2.5)x

f(x) = 2.5(1.2)x

Which graph is the sequence defined by the function f(x) = 3(2)x-1?

On a coordinate plane, 5 points are plotted. The points are (0, 2), (1, 6), (2, 18), (3, 54), (4, 162).

On a coordinate plane, 5 points are plotted. The points are (1, 2), (2, 6), (3, 18), (4, 54), (5, 162).

On a coordinate plane, 6 points are plotted. The points are (0, 3), (1, 6), (2, 12), (3, 24), (4, 48), (5, 96).

On a coordinate plane, 5 points are plotted. The points are (1, 3), (2, 6), (3, 12), (4, 24), (5, 48).

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

f(x) = 100(5)x

f(x) = 100(x)5

f(x) = 500(2)x

f(x) = 500(x)2

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

2.5

What is the common ratio of the sequence?-2, 6, -18, 54,...

−3

−2

Which table represents exponential growth?

A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 6, 8.

A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16.

A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 7, 11.

A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 6, 10.

Which is the graph of ?

Option

The table represents an exponential function.

One-fifth

Two-fifths

Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. When she began her study, the frog population was estimated at 1,200. Which function represents the frog population after x years?

f(x) = 1,200(1.03)x

f(x) = 1,200(0.03)x

f(x) = 1,200(0.97)x

f(x) = 1,200(0.97x)

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

On a coordinate plane, the point (0, 0.25) is graphed.

On a coordinate plane, the point (0.25, 0) is graphed.

On a coordinate plane, the point (0, 20) is graphed.

On a coordinate plane, the point (20, 0) is graphed.

Josiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equation represents the amount of money in Josiah’s account, y, after x years?

y = 360(1.3)x

y = 360(0.3)x

y = 360(0.03)x

y = 360(1.03)x

A sequence of numbers begins with 12 and progresses geometrically. Each number is the previous number divided by 2.

One-half

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

On a coordinate plane, the point (0, 3) is graphed.

On a coordinate plane, the point (0, 4) is graphed.

On a coordinate plane, the point (3, 0) is graphed.

On a coordinate plane, the point (4, 0) is graphed.

Which is the graph of f(x) = 0.5(4)x?

On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 1), (2, 8), (3, 32).

On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 4), (1, 16), (2, 64).

On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 1), (3, 8), (4, 16).

On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 1), (1, 8), (2, 32).

Which are true of the function f(x) = 49? Select three options.The domain is the set of all real numbers. The range is the set of all real numbers. The domain is x > 0.The range is y > 0.As x increases by 1, each y-value is one-seventh of the previous y-value.

The domain is the set of all real numbers.

The range is the set of all real numbers.

The domain is x > 0.

The range is y > 0.

As x increases by 1, each y-value is one-seventh of the previous y-value.

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

f(x) = 6

f(x) = −6

f(x) = (6)x − 1

f(x) = (−6)x − 1

Which equation represents an exponential function that passes through the point (2, 36)?

f(x) = 4(3)x

f(x) = 4(x)3

f(x) = 6(3)x

f(x) = 6(x)3

Two exponential functions are shown in the table.

The functions f(x) and g(x) are reflections over the x-axis.

The functions f(x) and g(x) are reflections over the y-axis.

The function f(x) is a decreasing function, and g(x) is an increasing function.

The function f(x) has a greater initial value than g(x).

Which is the graph of f(x) = 100(0.7)x?

On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100).

On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 9) and (0, 100).

On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 70) and (0, 100).

On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 30) and (0, 100).

Which graph represents a geometric sequence?

On a coordinate plane, 5 points are plotted. The points are (1, 1), (2, 3), (3, 5), (4, 7), (5, 9).

On a coordinate plane, 4 points are plotted. The points are (1, 1), (2, 2), (3, 4), (4, 8).

On a coordinate plane, 3 points are plotted. The points are (1, 2), (4, 4), (9, 6).

On a coordinate plane, 3 points are plotted. The points are (1, 1), (2, 4), (3, 9).

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