Question

A new shopping mall records 150 total shoppers on their first day of business. Each day after that, the number of shoppers is 15 percent more than the number of shoppers the day before.

Answer 1

The number of shoppers is an illustration of an exponential function.

The expression for the number of shoppers is: $\mathbf{f(n) = 150(1.15)^n}$

The given parameters are:

$\mathbf{a = 150}$ -- the number of shoppers on the first day of business

$\mathbf{r = 15\%}$ --- the rate

Because, the number of shoppers increases each day, the number of shopper on a certain day is:

$\mathbf{f(n) = a \times (1 + r)^n}$

Substitute 15% for r

$\mathbf{f(n) = a \times (1 + 15\%)^n}$

Express percentage as decimal

$\mathbf{f(n) = a \times (1 + 0.15)^n}$

$\mathbf{f(n) = a \times (1.15)^n}$

Substitute 150 for a

$\mathbf{f(n) = 150 \times (1.15)^n}$

$\mathbf{f(n) = 150(1.15)^n}$

Hence, the expression for the number of shoppers is: $\mathbf{f(n) = 150(1.15)^n}$

Read more about exponential functions at:

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