Question

1. annual sales for a restaurant were $575,000 in 2006. since then, the sales increased at a rate of 3% per year. write and use an exponential model to find the sales in 2018.

Explanation:

Step1: Define exponential growth formula

The exponential growth model is $A = P(1 + r)^t$, where:

• $P$ = initial amount, $r$ = annual growth rate, $t$ = time in years, $A$ = final amount

Step2: Identify given values

$P = 575000$, $r = 0.03$, $t = 2018 - 2006 = 12$

Step3: Substitute values into formula

$A = 575000(1 + 0.03)^{12}$

Step4: Calculate the growth factor

First compute $(1.03)^{12} \approx 1.42576$

Step5: Compute final sales

$A = 575000 \times 1.42576$

Answer:

$\approx 820,002$ (rounded to the nearest whole number, or $\$820,000$ when rounded to the nearest thousand)