Answered

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15. Annual sales for a surf shop are $130,000
and are increasing at a rate of 7% per year; 7 years
find the Function and the
Value after 7 years

Sagot :

elcharly64

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]

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