Question

3. The number of home phones Best Bytes sold

decreased by 14% each year after 1987. Write
a function to represent the number of home
phones sold x years after 1987.

Answer 1

`f(x)=a(0.86)^x`

where:

• a is the number of phones sold in 1987
• x is the number of years after 1987

Explanation:

General form of an exponential function:

`f(x)=ab^x`

where:

• a is the initial value
• b is the growth/decay factor in decimal form
• x is the independent variable
• f(x) is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Given:

• f(x) = number of home phones sold after 1987
• x = years after 1987
• a = number of phones sold in 1987

If the number of phones decreased by 14% each year, then each year the number of phones will be 86% of the previous year
(100% - 14% = 86%)

Therefore, b = 86% = 0.86

Substitute the given and found values into the general form of the function to create a function to represent the number of home phones sold:

`f(x)=a(0.86)^x`

where:

• a is the number of phones sold in 1987
• x is the number of years after 1987

Answer 2

Explanation:

Let the number of phones sold in 1987 is k.

The rate of decrease is

• 1 - 14% =
• 1 - 0.14 =
• 0.86

The function to represent the number of phones P sold after x years after 1987 is

• P(x) = k(0.86ˣ)