Chapter 6.1, Problem 52E

To determine

To find: number of grills that a store expects to sell in the year 6.

Answer to Problem 52E

Approximately $4681\text{ grills}$

Explanation of Solution

Given:

Grills sold last year = 3300

Increase in sale each year = 6%

Concept used:

Exponential function:

  $y=a{b}^x$.......(1)

Here, the y-values changes by a factor of b as x increases by 1 and the y intercept is a.

Let the variable x represent the year and the variable y represents the total sale for that year.

Also let the last year be represented by $x=0$ .

And the total sale of last year is $y=3300$ .

This implies that y-intercept is 3300.

Also it is given that the sales are increasing each year by 6%.

So, it can be said that as x increases by 1 the y-values changes by a factor of $1.06$ .

So, substituting $a=3300$ and $b=1.06$ in equation (1), the required exponential function is:

  $y=3300{\left(1.06\right)}^x$

Then, the total sale in the year 6 is found by substituting $x=6$ in the above function.

  $\begin{array}{c}y\left(6\right)=3300{\left(1.06\right)}^6\\ =3300\left(1.41852\right)\\ =4681.11\end{array}$

So, the total sale in the year 6 is about 4,681 gas grills.