Exponential Applications

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a(b)^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What does the base of an exponential function represent?

Back

The base of an exponential function indicates the growth (if greater than 1) or decay (if between 0 and 1) rate of the function.

Front

How do you calculate the percent increase in an exponential function?

Back

To calculate the percent increase, subtract 1 from the base (b) of the function, then multiply by 100. For example, if f(x) = a(1 + r)^x, the percent increase is r * 100.

Front

What is the percent decrease in the function f(x) = 250(0.95)^x?

Back

The percent decrease is 5%, calculated as (1 - 0.95) * 100.

Front

Write the equation for a value that appreciates by 6% annually starting at $350.

Back

f(x) = 350(1 + 0.06)^x.

Front

What does the equation T = 12,000(1.03)^x represent?

Back

This equation represents the tuition T after x years, starting from $12,000 and increasing by 3% each year.

Front

How do you determine the value of an exponential function after a certain number of years?

Back

Substitute the number of years into the function's equation to find the value.

Front

What is the percent increase for the function f(x) = 3000(1.17)^x?

Back

The percent increase is 17%, calculated as (1.17 - 1) * 100.

Front

If a function decreases by 5%, what is the base of the function?

Back

The base of the function is 0.95, since (1 - 0.05) = 0.95.

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a(1 + r)^x, where 'r' is the growth rate.