Answer:
[tex]f(x)=a(0.86)^x[/tex]
where:
- a is the number of phones sold in 1987
- x is the number of years after 1987
Step-by-step explanation:
General form of an exponential function:
[tex]f(x)=ab^x[/tex]
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:
[tex]f(x)=a(0.86)^x[/tex]
where:
- a is the number of phones sold in 1987
- x is the number of years after 1987
