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On the day that a certain celebrity proposes marriage, 10 people know about it. Each day afterward, the number of people who know triples.
Write a function that gives the total number
n(t) of people who know about the celebrity proposing
t days after the celebrity proposes.

n(t)=

On the day that a certain celebrity proposes marriage, $10$ people know about it. Each day afterward, the number of people who know triples. $\newline$ Write a function that gives the total number $n(t)$ of people who know about the celebrity proposing $t$ days after the celebrity proposes. $\newline$ $n(t)=$

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Write exponential functions: word problems

Full solution

Q. On the day that a certain celebrity proposes marriage,

10

people know about it. Each day afterward, the number of people who know triples.

\newline

Write a function that gives the total number

n(t)

of people who know about the celebrity proposing

t

days after the celebrity proposes.

\newline

n(t)=

Identify initial condition: Identify the initial condition. $\newline$ On the day the celebrity proposes ( $t = 0$ ), $10$ people know about it. This is our initial condition for the function $n(t)$ .
Determine growth pattern: Determine the pattern of growth. $\newline$ Each day after the proposal, the number of people who know triples. This indicates an exponential growth pattern.
Write exponential growth function: Write the function based on the pattern. $\newline$ Since the number of people triples each day, we can express this growth as $3$ raised to the power of $t$ (the number of days). To include the initial condition, we multiply this by the initial number of people, which is $10$ . Therefore, the function is $n(t) = 10 \times 3^t$ .

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