Question

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) =

Explanation:

Step1: Identify initial value

Initial number of people: $n(0)=10$

Step2: Recognize exponential growth type

This is exponential growth where quantity triples daily, so the growth factor is $3$. The general form of an exponential function is $n(t) = \text{Initial Value} \times (\text{Growth Factor})^t$.

Step3: Substitute values into formula

Substitute initial value $10$ and growth factor $3$ into the formula.
$n(t)=10 \times 3^t$

Answer:

$n(t)=10 \cdot 3^t$