Exponential Growth and Decay Problems

Front

What is the formula for exponential decay?

Back

Front

Define half-life in the context of exponential decay.

Back

Half-life is the time required for a quantity to reduce to half its initial value. It is commonly used in radioactive decay and pharmacokinetics.

Front

What is the initial value in the function f(t) = 200(0.9)^t?

Back

The initial value is 200.

Front

Write the exponential growth equation for an initial amount of 100 with a growth rate of 20% per year.

Back

Front

How do you determine the remaining amount after a certain time using the half-life concept?

Back

Front

What does the base of an exponential function represent in growth and decay?

Back

In growth, the base is greater than 1, indicating an increase. In decay, the base is between 0 and 1, indicating a decrease.

Front

If a population of bacteria doubles every 3 hours, what is the growth factor?

Back

The growth factor is 2, as the population doubles.

Front

What is the formula for calculating the amount remaining after exponential decay?

Back

Front

How do you convert a percentage decay rate to a decimal for calculations?

Back

To convert a percentage decay rate to a decimal, divide by 100. For example, a 25% decay rate becomes 0.25.

Front

What is the formula for continuous exponential growth?

Back