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Mapiya writes a series of novels. She earned
$75,000 for the first book, and her cumulative earnings double with each sequel that she writes.
Write a function that gives Mapiya's cumulative earnings
E(n), in dollars, when she has written
n sequels.
Do not enter commas in your answer.

E(n)=

Mapiya writes a series of novels. She earned $\$ 75,000$ for the first book, and her cumulative earnings double with each sequel that she writes. $\newline$ Write a function that gives Mapiya's cumulative earnings $E(n)$ , in dollars, when she has written $n$ sequels. $\newline$ Do not enter commas in your answer. $\newline$ $E(n)=$

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Write exponential functions: word problems

Full solution

Q. Mapiya writes a series of novels. She earned

\$ 75,000

for the first book, and her cumulative earnings double with each sequel that she writes.

\newline

Write a function that gives Mapiya's cumulative earnings

E(n)

, in dollars, when she has written

n

sequels.

\newline

Do not enter commas in your answer.

\newline

E(n)=

Mapiya's Earnings: Mapiya's earnings for the first book are $\$75,000$ . Since her cumulative earnings double with each sequel, we can express her earnings as a function of the number of sequels written using powers of $2$ . For the first book ( $0$ sequels), her earnings are $\$75,000$ . For each sequel written, we multiply the previous total by $2$ . This can be expressed as $E(n) = \$75,000 \times 2^n$ , where $n$ is the number of sequels written.
Expressing Earnings as a Function: To ensure the function is correct, let's check a few values. If Mapiya writes $1$ sequel, her cumulative earnings should be $\$75,000 \times 2^1 = \$150,000$ . If she writes $2$ sequels, her cumulative earnings should be $\$75,000 \times 2^2 = \$300,000$ . These checks are consistent with the doubling pattern described.
Checking the Function: The final function for Mapiya's cumulative earnings $E(n)$ when she has written $n$ sequels is $E(n) = 75000 \times 2^n$ .

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