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S(y)=28(1.13)^(12 y)
The function models
S, the number of paying supporters a podcast has,
y years after the podcast's launch. Based on the function, what is the monthly percent increase in the number of paying supporters?
Choose 1 answer:
(A)
12%
(B)
13%
(C)
28%
(D)
113%

$S(y)=28(1.13)^{12 y}$ $\newline$ The function models $S$ , the number of paying supporters a podcast has, $y$ years after the podcast's launch. Based on the function, what is the monthly percent increase in the number of paying supporters? $\newline$ Choose $1$ answer: $\newline$ (A) $12 \%$ $\newline$ (B) $13 \%$ $\newline$ (C) $\mathbf{2 8 \%}$ $\newline$ (D) $113 \%$

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Write exponential functions: word problems

Full solution

Q.

S(y)=28(1.13)^{12 y}

\newline

The function models

S

, the number of paying supporters a podcast has,

y

years after the podcast's launch. Based on the function, what is the monthly percent increase in the number of paying supporters?

\newline

Choose

1

answer:

\newline

(A)

12 \%

\newline

(B)

13 \%

\newline

(C)

\mathbf{2 8 \%}

\newline

(D)

113 \%

Identify Function: The function provided is $S(y) = 28(1.13)^{12y}$ . This function represents exponential growth, where the base of the exponent, $1.13$ , indicates the growth factor for each period. Since the exponent is $12y$ , this suggests that the growth factor is applied $12$ times per year, or monthly. To find the monthly percent increase, we need to look at the base of the exponent, which is $1.13$ .
Calculate Monthly Increase: The base $1.13$ can be converted to a percentage by subtracting $1$ and then multiplying by $100$ . This will give us the percent increase per month. $\newline$ Calculation: $(1.13 - 1) \times 100 = 0.13 \times 100 = 13\%$
Match with Options: Now that we have calculated the monthly percent increase, we can match our result with the given options. $\newline$ The correct answer is (B) $13\%$ .

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