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The projected value of an investment is modeled by the exponential function V(t)=30,000(1.125)t𝑉(𝑡)=30,000(1.125)𝑡, where V(t)𝑉(𝑡) is the total value after t𝑡 years. What is the percent increase each year for the investment?

Question

The projected value of an investment is modeled by the exponential function V(t)=30,000(1.125)t𝑉(𝑡)=30,000(1.125)𝑡, where V(t)𝑉(𝑡) is the total value after t𝑡 years. What is the percent increase each year for the investment?

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Solution

The percent increase each year for the investment is 12.5%. This is because in the exponential function V(t)=30,000(1.125)^t, the base of the exponent, 1.125, represents a 12.5% increase each year. This is calculated by subtracting 1 from 1.125 and multiplying by 100 to convert the decimal to a percentage.

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