Exponential functions

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 it mean for a function to exhibit exponential growth?

Back

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

Front

What does it mean for a function to exhibit exponential decay?

Back

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

Front

Identify the initial value in the function y = 5(3)^x.

Back

The initial value is 5.

Front

In the function A = 10(0.5)^t, is this growth or decay?

Back

This is exponential decay.

Front

What is the base in the function f(x) = 2(4)^x?

Back

The base is 4.

Front

How do you determine if a function is exponential growth or decay from its equation?

Back

If the base is greater than 1, it is exponential growth; if the base is between 0 and 1, it is exponential decay.

Front

What is the formula for calculating the amount after t time periods in exponential growth?

Back

A = P(1 + r)^t, where A is the amount, P is the principal, r is the rate, and t is time.

Front

What is the formula for calculating the amount after t time periods in exponential decay?

Back

A = P(1 - r)^t, where A is the amount, P is the principal, r is the rate, and t is time.

Front

What is the significance of the exponent in an exponential function?

Back

The exponent indicates the number of time periods that have passed and affects the growth or decay of the function.