Question

On the day that a certain celebrity proposes marriage, 101010 people know about it. Each day afterward, the number of people who know triples. Write a function that gives the total number n(t)n(t)n, left parenthesis, t, right parenthesis of people who know about the celebrity proposing ttt days after the celebrity proposes.

Answer 1

n(t) = 101010(3^t)

Explanation:

The initial number of people who knew about it is;

n(0) = 101010

The number of people who will have known in a day's time;

n(1) = 101010(3)

The number of people who will have known in 2 day's time;

n(2) = 101010(3)(3) = 101010(3^2)

The number of people who will have known in 3 day's time;

n(3) = 101010(3)(3)(3) = 101010(3^3)

Therefore, the total number n(t) of people who know about the celebrity proposing t days after the celebrity proposes becomes;

n(t) = 101010(3^t)

Answer 2

On the day that a certain celebrity proposes marriage, 10 people know about it. Each day afterward, the number of people who know triples. The function n(t) can be denoted in two ways.

Condition 1: If the day of the proposal is being t=1

The function is :
`n(t)=10(3^(t-1) )`

Condition 2: Considering the next day as the first day after the proposal then the initial day was day zero and the function is:

`n(t)=10(3^(t) )`

Checking: when t = 1, n(t) = 10; when t = 2, n(t) = 30; when t = 3, n(t) = 90 and so on.