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 is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases by a constant percentage over time, while exponential decay occurs when a quantity decreases by a constant percentage over time.

Front

What is the general form of an exponential growth function?

Back

The general form is f(t) = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the general form of an exponential decay function?

Back

The general form is f(t) = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

If a population of bears decreases by 2% each year, what is the decay rate in decimal form?

Back

The decay rate in decimal form is 0.02.

Front

How do you represent a population that decreases by a percentage each year?

Back

You represent it using the function B = a(1 - r)^t, where 'a' is the initial population, 'r' is the decay rate, and 't' is time.

Front

What does the base of an exponential function represent?

Back

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

Front

What is the value of a home worth today if it was purchased for $160,000 and appreciates at 5% per year for 20 years?

Back

The home is worth approximately $424,527.63 today.

Front

What does it mean if an exponential function has a base greater than 1?

Back

If the base is greater than 1, the function represents exponential growth.

Front

What does it mean if an exponential function has a base between 0 and 1?

Back

If the base is between 0 and 1, the function represents exponential decay.