We have been given that annual sales for a fast food restaurant are $650,000 and are increasing at rate of 4% per year. We are asked to find the annual sales after 7 years using an exponential function.
We know that an exponential growth function is in form [tex]y=a(1+r)^x[/tex], where,
y = Final amount,
a = Initial amount,
r = Growth rate in decimal form,
x = Time.
Let us convert 4% into decimal form.
[tex]4\%=\frac{4}{100}=0.04[/tex]
Initial value is $650,000.
[tex]y=\$650,000(1+0.04)^x[/tex]
[tex]y=\$650,000(1.04)^x[/tex]
To find annual sales after 7 years, we will substitute [tex]x=7[/tex] in our function as:
[tex]y=\$650,000(1.04)^7[/tex]
[tex]y=\$650,000(1.31593177923584)[/tex]
[tex]y=\$855,355.656503296[/tex]
Upon rounding to nearest hundredths, we will get:
[tex]y\approx \$855,355.66[/tex]
Therefore, the annual sales will be approximately [tex]\$855,355.66[/tex] after 7 years.
