The number of shoppers is an illustration of an exponential function.
The expression for the number of shoppers is: [tex]\mathbf{f(n) = 150(1.15)^n}[/tex]
The given parameters are:
[tex]\mathbf{a = 150}[/tex] -- the number of shoppers on the first day of business
[tex]\mathbf{r = 15\%}[/tex] --- the rate
Because, the number of shoppers increases each day, the number of shopper on a certain day is:
[tex]\mathbf{f(n) = a \times (1 + r)^n}[/tex]
Substitute 15% for r
[tex]\mathbf{f(n) = a \times (1 + 15\%)^n}[/tex]
Express percentage as decimal
[tex]\mathbf{f(n) = a \times (1 + 0.15)^n}[/tex]
[tex]\mathbf{f(n) = a \times (1.15)^n}[/tex]
Substitute 150 for a
[tex]\mathbf{f(n) = 150 \times (1.15)^n}[/tex]
[tex]\mathbf{f(n) = 150(1.15)^n}[/tex]
Hence, the expression for the number of shoppers is: [tex]\mathbf{f(n) = 150(1.15)^n}[/tex]
Read more about exponential functions at:
https://brainly.com/question/11487261
