Writing Exponential Functions (Word Problems)

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 the base of an exponential function represent?

Back

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

Front

How do you determine the growth rate from an exponential function?

Back

The growth rate can be determined by subtracting 1 from the base of the function. For example, in f(x) = a(1 + r)^x, r is the growth rate.

Front

What is the decay rate in the function f(x) = 800(0.85)^x?

Back

The decay rate is 15%, which is calculated as 1 - 0.85.

Front

How do you write an exponential function for a situation involving growth?

Back

To write an exponential function for growth, use the formula C(t) = C_0(1 + r)^t, where C_0 is the initial amount, r is the growth rate, and t is time.

Front

What is the formula to calculate the future value of an investment with exponential growth?

Back

The future value can be calculated using 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 annual interest rate, and t is the number of years.

Front

What is the decay factor in the function f(x) = 15000(0.92)^x?

Back

The decay factor is 0.92, which represents the percentage of the value retained after each time period.

Front

How do you find the value of an investment after a certain number of years with exponential decay?

Back

Use the formula A = P(1 - r)^t, where A is the amount after time t, P is the initial amount, r is the decay rate, and t is the time.

Front

What does it mean if an investment has a decay rate of 8%?

Back

It means that the investment loses 8% of its value each year.

Front

What is the initial value in the function y = 24220(0.85)^x?

Back

The initial value is $24,220, which is the value of the investment at x = 0.