Exponential Growth and Decay Word Problems

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over a period of time, resulting in a rapid increase.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a fixed percentage over a period of time, leading to a rapid decrease.

Front

Given the function f(x) = 1.5^x, what is the percent of growth?

Back

50%.

Front

Given the function f(x) = 0.92^x, is this a growth or decay function?

Back

Decay.

Front

How do you determine if a function represents growth or decay?

Back

If the base of the exponential function is greater than 1, it represents growth; if the base is between 0 and 1, it represents decay.

Front

What is the formula for exponential decay?

Back

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

Front

What is the formula for exponential growth?

Back

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

Front

Given the function f(x) = 10(0.45)^x, what is the percent of decrease?

Back

55%.

Front

If a book is worth $58 and depreciates at a rate of 7% per year, what is the value after 8 years?

Back

$32.46, using f(t) = 58(0.93)^t.

Front

What does the term 'percent of decrease' mean?

Back

It refers to the percentage by which a quantity reduces over a specific period.