Exponential Growth and Decay Applications

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 is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

Front

Write the general formula for exponential growth.

Back

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

Front

Write the general formula for exponential decay.

Back

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

Front

What does the base of an exponential function represent?

Back

The base indicates the growth or decay factor; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

If a population doubles every 3 years, what is the growth factor?

Back

The growth factor is 2, as the population doubles.

Front

How do you calculate the percent increase in an exponential function?

Back

Percent increase = (final value - initial value) / initial value * 100%.

Front

How do you calculate the percent decrease in an exponential function?

Back

Percent decrease = (initial value - final value) / initial value * 100%.

Front

What is the formula for continuous compounding?

Back

A = Pe^(rt), where 'A' is the amount, 'P' is the principal, 'e' is Euler's number, 'r' is the rate, and 't' is time.

Front

What is the half-life in exponential decay?

Back

Half-life is the time required for a quantity to reduce to half its initial value.