Exponential Application Practice

Front

What is exponential decay?

Back

Exponential decay refers to a decrease in quantity where the rate of decrease is proportional to the current amount, often modeled by the equation y = a(1 - r)^t.

Front

How do you identify if a problem represents growth or decay?

Back

If the quantity decreases over time, it represents decay; if it increases, it represents growth.

Front

What is the general formula for exponential growth?

Back

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

Front

What does the 'b-value' in an exponential function represent?

Back

The 'b-value' represents the growth or decay factor in the function f(x) = a(b^x), where b > 1 indicates growth and 0 < b < 1 indicates decay.

Front

What is the formula for calculating the total amount with compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the total amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

How do you calculate the rate of decay from a given exponential function?

Back

The rate of decay can be calculated as (1 - r) where r is the decay factor in the function y = a(1 - r)^t.

Front

What is the significance of the interest rate in a compound interest problem?

Back

The interest rate determines how much the principal amount will grow over time when compounded, affecting the total amount paid or received.

Front

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

Back

To convert a percentage growth rate to a decimal, divide the percentage by 100. For example, 16% becomes 0.16.

Front

What is the difference between simple interest and compound interest?

Back

Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus any interest that has been added to it.

Front

What does it mean for a population to decrease by a certain percentage per year?

Back

It means that each year, the population is reduced by that percentage of its current size.