Exponential Growth and Decay

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 as the quantity grows larger.

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 as the quantity becomes smaller.

Front

What is the general formula for exponential growth?

Back

The general formula is 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 formula for exponential decay?

Back

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

Front

In the function y = 1500(0.985)^t, what does 1500 represent?

Back

1500 represents the initial population of deer.

Front

In the function y = 5000(0.98)^x, what does 0.98 represent?

Back

0.98 represents the remaining percentage of money in the account after each year.

Front

How do you convert a percentage decrease to a decimal for use in exponential decay?

Back

To convert a percentage decrease to a decimal, subtract the percentage from 100% and then divide by 100. For example, a 14.9% decrease becomes 0.851.

Front

What does the term 'initial value' mean in exponential functions?

Back

The initial value is the starting amount before any growth or decay occurs.

Front

What is the significance of the exponent in exponential functions?

Back

The exponent represents the number of time periods that have passed, affecting the total amount through repeated multiplication.

Front

How can you determine the growth or decay rate from an exponential function?

Back

The growth or decay rate can be found by subtracting 1 from the base of the exponent in the function.