Growth and Decay Functions

In the equation y = a(b)^x, what does a represent?

• Amount you multiply by

• Starting (initial) amount

• Exponential function

• Slope

The function f (x) = 500(1.035)^x models the amount of money in a certificate of deposit after x years. How much money will there be in 6 years?

• $1.23

• $517.50

• $483.10

• $614.63

The function f (x) = 200,000(0.98)^x, where x is the time in years, models the population of a city. What will the population be in 7 years?

• 173,625 people

• 300,000 people

• 416,423 people

• 830,509 people

Which set of ordered pairs satisfies an exponential function?

• {(–1, –64), (0, 0), (1, 64), (2, 128)}

• {(0, 4), (1, 12), (2, 36), (3, 108)}

• {(–1, 1), (0, 0), (1, 1), (2, 4)}

• {(–1, 1), (0, 0), (1, 1), (2, 4)}

Identify the initial value:

y = 6.87(4)^x

• 4

• 6.87

• 3

• 1

The function y = 125(1.13)^x represents Mr. Gantz's recent investments where x is measured in years. Which is not true?

• Mr. Gantz initially invested $125

• After 4 years, Mr. Gantz will have about $203.81

• Mr. Gantz earns more money in year 1 than in year 5

Identify the y-intercept (initial value) in the function

f (x) = 13(0.27)^x

• (0.27)^x

• 0.27

• 13

• 3.51

Identify the y-intercept (initial value) of the function

f (x) = 2(4)^x.

• 2

• 4

• (2)^x

• 8

Identify the common ratio (multiplier) of the function

f (x) = 2(4)^x.

• 2

• 4

• (2)^x

• 8

What is a, the starting term, for the function

f (x) = 300(1.16)^x?

• 300

• 1.16

• 0.16

• x