Exponential Growth and Decay Word Problems

Front

What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate over time.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to a decrease that slows over time.

Front

What is the formula for exponential growth?

Back

The formula is f(t) = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the formula for exponential decay?

Back

The formula is f(t) = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

How do you determine the rate of change in an exponential function?

Back

The rate of change can be determined by the base of the exponential function. For f(x) = a(b^x), the rate of change is (b - 1) * 100%.

Front

If something changes at a rate of 5% every two minutes, what is 't' for a time period of 35 minutes?

Back

t = 17.5 (since 35 minutes / 2 minutes = 17.5 intervals).

Front

Given the function f(x) = 1.00005^x, what is the rate of change?

Back

The rate of change is 0.005%.

Front

How can you identify 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

Given the function f(x) = 0.0000000435^x, is this a growth or decay function?

Back

This is a decay function.

Front

Given the function f(x) = 1.07^x, what is the rate of decay?

Back

The rate of decay is 7%.