Growth and Decay

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is given by: y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate (as a decimal), and 't' is the time.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is given by: y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate (as a decimal), and 't' is the time.

Front

How do you calculate the remaining amount after a decay percentage?

Back

To calculate the remaining amount after a decay percentage, use the formula: Remaining Amount = Initial Amount * (1 - Decay Rate)^Time.

Front

How do you calculate the future population given a growth rate?

Back

To calculate the future population, use the formula: Future Population = Current Population * (1 + Growth Rate)^Years.

Front

What does a growth rate of 4% mean in mathematical terms?

Back

A growth rate of 4% means that the population increases by 4% of its current value each year, or mathematically, it can be represented as a multiplier of 1.04.

Front

What does a decay rate of 13.2% mean in mathematical terms?

Back

A decay rate of 13.2% means that the remaining amount decreases by 13.2% of its current value each time period, or mathematically, it can be represented as a multiplier of 0.868.

Front

If a population is modeled by f(x)=6191(1.04)^x, what does 1.04 represent?

Back

In the function f(x)=6191(1.04)^x, the 1.04 represents a growth factor of 4%, indicating that the population increases by 4% each year.

Front

What is the initial amount in the function y = 15(1.35)^x?

Back

The initial amount in the function y = 15(1.35)^x is $15.

Front

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

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 4% becomes 0.04.

Front

What is the difference between growth and decay functions?

Back

Growth functions increase over time, represented by a base greater than 1, while decay functions decrease over time, represented by a base less than 1.