Find this year's and next year's sales. Then, use them to write a general equation.
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Practice makes perfect
We know that last year 3300 gas grills were purchased. The store expects grill sales to increase by 6 % each year. With these in mind, let's write the expression for this year's expected sales.
3300+ 3300 * 0.06 ⇔ 3300(1+ 0.06)
Similarly, let's write the sales of the next few years, assuming 0 is the last year.
Years
Previous Year's Sales
Expected Sales
Rewrite
0
-
-
3300(1+0.06)^0
1
3300
3300(1+ 0.06)
3300(1+0.06)^1
2
3300(1+0.06)
3300(1+0.06)(1+ 0.06)
3300(1+0.06)^2
3
3300(1+0.06)^2
3300(1+0.06)^2(1+ 0.06)
3300(1+0.06)^3
We see that the exponent of the term (1+0.06) increases as the years increase. Hence, we can write the equation below.
y=3300(1+0.06)^x
Here, x represents the number of years and y represents the expected number of sales. To find the sales in Year 6, we will substitute 6 for x into the function y=3300(1+0.06)^x.
