Exponential Growth and Decay

Front

What is exponential growth?

Back

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

Front

Identify the formula for exponential growth.

Back

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

Front

Identify the formula for exponential decay.

Back

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

Front

What does the variable 'a' represent in exponential functions?

Back

'a' represents the initial value or starting amount before growth or decay occurs.

Front

What does the variable 'r' represent in exponential functions?

Back

'r' represents the rate of growth (positive) or decay (negative) expressed as a decimal.

Front

How do you calculate the value after 8 years of a printer worth $35,000 depreciating at 5% per year?

Back

Use the formula: y = 35000(1 - 0.05)^8, which results in approximately $23,219.72.

Front

What is the initial value in the function f(x) = 300(1.16)^x?

Back

The initial value is 300.

Front

If a population of bacteria doubles every 3 hours, what type of growth is this?

Back

This is an example of exponential growth.

Front

If a car's value decreases by 15% each year, what type of change is this?

Back

This is an example of exponential decay.