The function V(t)=1.50(1.17)^t represents the value V(t) in dollars, of a comic book t years after its purchase in 2000. What is the annual growth rate of the comic book? 1.50% 1.17% 17% 117%

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The function V(t)=1.50(1.17)^t represents the value V(t) in dollars, of a comic book t years after its purchase in 2000. What is the annual growth rate of the comic book? 1.50% 1.17% 17% 117%

Answer 1

To find the annual growth rate of the comic book's value, we need to look at the function \(V(t)=1.50(1.17)^{t}\). The function represents exponential growth, where the base of the exponent, \(1.17\), indicates the growth factor per year.The growth factor can be converted to a percentage growth rate by subtracting 1 from the growth factor and then multiplying by 100. This is because the growth factor includes the original amount (100%) plus the percentage increase.Let's calculate the annual growth rate:\[\text{Growth factor} = 1.17\]To find the growth rate as a percentage, subtract 1 from the growth factor:\[\text{Growth rate} = (1.17 - 1) \times 100\%\]\[\text{Growth rate} = 0.17 \times 100\%\]\[\text{Growth rate} = 17\%\]Therefore, the annual growth rate of the comic book is **17%**.

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The function V(t)=1.50(1.17)^t represents the value V(t) in dollars, of a comic book t years after its purchase in 2000. What is the annual growth rate of the comic book? 1.50% 1.17% 17% 117%

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