Exponential Functions - Graphs & Tables

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. It shows rapid growth or decay.

Front

What does the 'a' represent in an exponential function?

Back

In an exponential function, 'a' represents the y-intercept, which is the value of the function when x = 0.

Front

What is the y-intercept of the function y = 3(2^x)?

Back

The y-intercept is (0, 3).

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is y = a(b^x) where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is y = a(b^x) where 0 < b < 1.

Front

How do you calculate the value of an investment that grows exponentially?

Back

Use the formula A = P(1 + r)^t, where A is the amount of money accumulated after n years, P is the principal amount, r is the rate of interest, and t is the time in years.

Front

If a printer depreciates at a rate of 5% per year, what is the formula to find its value after t years?

Back

The formula is V = P(1 - r)^t, where V is the value after t years, P is the initial value, and r is the rate of depreciation.

Front

What is the value of an item worth $1000 after 3 years if it depreciates at 10% per year?

Back

The value is approximately $729.00.

Front

What does the base 'b' in an exponential function indicate?

Back

The base 'b' indicates the growth factor in an exponential function. If b > 1, the function represents growth; if 0 < b < 1, it represents decay.

Front

What is the approximate value of land purchased for $30,000 that appreciates at 5% per year after 51 years?

Back

The approximate value is $361,223.09.