5.3 exponential growth and decay

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over a specific 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 specific period of time, leading to a rapid decrease.

Front

What is the formula for exponential growth?

Back

The formula is: A = P(1 + r)^t, where A is the amount after time t, P 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: A = P(1 - r)^t, where A is the amount after time t, P is the initial amount, r is the decay rate, and t is time.

Front

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

Back

The growth factor is 2.

Front

How do you calculate the decay factor?

Back

The decay factor is calculated as 1 - r, where r is the decay rate.

Front

What is the initial amount in an exponential equation?

Back

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

Front

What does a decay rate of 8% mean?

Back

It means that each year, the value decreases to 92% of its previous value.

Front

How do you model a situation of exponential growth?

Back

You can model it using the formula A = P(1 + r)^t, substituting the values for P, r, and t.

Front

What is the significance of the time variable in exponential functions?

Back

The time variable determines how many periods of growth or decay occur, affecting the final amount.