Exponential Growth and Decay

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is y = a(1 + r)^t, where y is the final amount, a is the initial amount, r is the growth rate (as a decimal), and t is the time in years.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is y = a(1 - r)^t, where y is the final amount, a is the initial amount, r is the decay rate (as a decimal), and t is the time in years.

Front

If a population of fish starts at 8,000 and increases by 6% per year, what is the population after 10 years?

Back

The population after 10 years can be calculated using the formula: y = 8000(1 + 0.06)^{10}, which equals approximately 14,327.

Front

How do you calculate the depreciation of an asset?

Back

To calculate the depreciation of an asset, use the formula: y = a(1 - r)^t, where y is the value after t years, a is the initial value, r is the depreciation rate (as a decimal), and t is the time in years.

Front

What is the difference between growth and decay in exponential functions?

Back

In exponential growth, the quantity increases over time, while in exponential decay, the quantity decreases over time.

Front

What does the variable 't' represent in exponential functions?

Back

The variable 't' represents time, usually measured in years, in exponential functions.

Front

What is the initial amount in an exponential function?

Back

The initial amount in an exponential function is the value of the quantity at time t = 0, denoted as 'a' in the formulas.

Front

How do you convert a percentage to a decimal for use in exponential functions?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 6% becomes 0.06.

Front

What is the significance of the base in exponential functions?

Back

The base in exponential functions (1 + r for growth and 1 - r for decay) determines the rate at which the quantity increases or decreases.

Front

How can you determine the population after a certain number of years using exponential functions?

Back

You can determine the population after a certain number of years by substituting the time value into the exponential growth or decay formula.