Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate over time.

Front

What is exponential decay?

Back

Exponential decay refers to the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

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

How do you calculate the future value of an investment with exponential growth?

Back

Use the formula A = P(1 + r)^t, substituting P for the initial investment, r for the growth rate, and t for the number of years.

Front

How do you calculate the future value of an asset with exponential decay?

Back

Use the formula A = P(1 - r)^t, substituting P for the initial value, r for the decay rate, and t for the number of years.

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 fish decreases by 6% per year, what type of change is this?

Back

This is an example of exponential decay.

Front

What is the value of an asset after 8 years if it depreciates at 5% per year and starts at $35,000?

Back

The value after 8 years is $23,219.72.

Front

How do you determine if a situation represents growth or decay?

Back

If the percentage change is positive, it represents growth; if negative, it represents decay.