Exponential Functions (percent growth or decay)

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = 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 in an exponential function represent?

Back

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

Front

What is the initial amount in the exponential function y = 0.5(1.081)^x?

Back

The initial amount is 0.5.

Front

How do you determine if an exponential function represents growth or decay?

Back

If the base is greater than 1, the function represents growth. If the base is between 0 and 1, it represents decay.

Front

What is the percent growth in the function y = 50(1.07)^x?

Back

The percent growth is 7%.

Front

What is the percent decay in the function y = 1000(0.65)^x?

Back

The percent decay is 35% (calculated as 1 - 0.65 = 0.35 or 35%).

Front

In the function y = a(b^x), what does 'a' represent?

Back

'a' represents the initial amount or starting value of the function.

Front

What is the formula to calculate percent growth from the base of an exponential function?

Back

Percent growth = (base - 1) * 100%.

Front

What is the formula to calculate percent decay from the base of an exponential function?

Back

Percent decay = (1 - base) * 100%.

Front

If y = 200(1.05)^x, what is the initial amount?

Back

The initial amount is 200.