Answer:
[tex]P(7)=\$208,752[/tex]
Step-by-step explanation:
Exponential Growth
The natural growth of some magnitudes can be modeled by the equation:
[tex]P(t)=P_o(1+r)^t[/tex]
Where P(t) is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.
It's given the annual sales for a surf shop are Po=$130,000. They are increasing at a rate of r=7% = 0.07 per year. Substituting values, the function is:
[tex]P(t)=\$130,000(1+0.07)^t[/tex]
[tex]\boxed{P(t)=\$130,000(1.07)^t}[/tex]
The value of the function after t=7 years is
[tex]P(7)=\$130,000(1.07)^7[/tex]
Computing:
[tex]P(7)=\$130,000*1.6058[/tex]
[tex]\mathbf{P(7)=\$208,752}[/tex]
