#45.5 Exponential Growth and Decay Refresher Lesson

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. For example, if a salary increases by 5% each year, it grows exponentially.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over time, leading to a rapid decrease. For example, if a car depreciates by 12% each year, its value decreases exponentially.

Front

What does 'a' represent in the exponential equation y=a(1-r)^x?

Back

In the equation, 'a' represents the initial value or starting amount before any growth or decay occurs.

Front

What does 'r' represent in the exponential equation y=a(1-r)^x?

Back

In the equation, 'r' represents the rate of growth or decay expressed as a decimal.

Front

How do you convert a percentage to a decimal?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 12% becomes 0.12.

Front

What is the formula for exponential decay?

Back

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

Front

What is the formula for exponential growth?

Back

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

Front

In the equation y=46000(1.05)^x, what does 'x' represent?

Back

In this equation, 'x' represents the time in years.

Front

In the equation y=13000(0.88)^x, what does 'y' represent?

Back

In this equation, 'y' represents the car's value in dollars after 'x' years.

Front

If a car is bought for $13,000 and depreciates at 12% annually, what is the value after 1 year?

Back

The value after 1 year is y = 13000(0.88)^1 = $11,440.