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. show all steps.

Explanation:

Step1: Define exponential growth model

The general exponential growth formula 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 model

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

Step4: Calculate growth factor

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

Step5: Compute final sales

$A = 575000 \times 1.42576$

Answer:

$\approx 819812$ dollars