Exponential Functions Review

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 of an exponential function indicate?

Back

The base of an exponential function indicates the growth or decay factor. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, resulting in a rapid decrease.

Front

How do you identify exponential growth or decay from a function?

Back

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

Front

What is the formula for compound interest?

Back

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

Front

If Riley invests $1,000 at 6.75% interest compounded semi-annually, how much will he have after 15 years?

Back

$2,706.86

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, as x can take any value.

Front

What is the range of an exponential function?

Back

The range of an exponential function is all positive real numbers, as the output (y) is always greater than zero.

Front

What does the graph of an exponential growth function look like?

Back

The graph of an exponential growth function rises steeply to the right and approaches the x-axis but never touches it.