Modeling Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time.

Front

What is the general formula for exponential growth?

Back

The general formula is y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time.

Front

What is exponential decay?

Back

Exponential decay occurs when the decrease in a value is proportional to its current value, leading to a rapid decline over time.

Front

What is the general formula for exponential decay?

Back

The general formula is y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the time.

Front

How do you convert a percentage to a decimal?

Back

To convert a percentage to a decimal, divide the percentage by 100.

Front

What is the growth rate in the equation y = 5(1.27)^x?

Back

The growth rate is 27%.

Front

What is the decay rate in the equation y = 35(0.65)^x?

Back

The decay rate is 35%.

Front

How do you find the decay rate from an exponential decay model?

Back

The decay rate can be found by subtracting the base of the exponent from 1.

Front

Write the equation for a model with an initial amount of 6 and a growth rate of 14%.

Back

y = 6(1 + 0.14)^x.

Front

What does the base of an exponential function represent?

Back

The base represents the growth or decay factor; values greater than 1 indicate growth, while values between 0 and 1 indicate decay.