Exponential Functions Flashcard Review

Front

What does the value 1.015 represent in the expression 12(1.015)^t for population modeling?

Back

The number of elephants increases by 1.5% each year.

Front

What percentage is the colony of ants decaying in the function f(x) = 800(0.87)^x?

Back

13%.

Front

What type of function is represented by a graph that shows a decrease over time?

Back

Decay.

Front

Which function represents an initial amount of $15 and an increase of 35% each year?

Back

y = 15(1.35)^x.

Front

Write an equation for the exponential function that has a base of 2 and an initial amount of 5.

Back

y = 5(2)^x.

Front

What is the general form of an exponential growth function?

Back

y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Front

What is the general form of an exponential decay function?

Back

y = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

Front

If a population doubles every 5 years, what is the growth factor?

Back

The growth factor is 2.

Front

How do you determine the decay rate from a decay function like f(x) = 800(0.87)^x?

Back

The decay rate is 1 - 0.87 = 0.13 or 13%.

Front

What does the base of an exponential function indicate?

Back

The base indicates the growth or decay factor per time unit.