Question

Every day, there are 3 times more likes on an internet video of a cat which is modeled by the function c(n) = (3)n − 1, where n is the number of days since the video posted. On the first day, there were 143 likes. What is the function that shows the number of likes each day?

Answer 1

The options are:

A.
`c(n) = (3)(143)^(n-1)`

B.
`c(n) = 143^(n-1)`

C. c(n) = (3)143 − n

D.
`143(3)^(n-1)`

SInce, The video of a cat is modeled by the function
`(3)^(n-1)`

Let us consider the A option.

`c(n) = (3)(143)^(n-1)`

When n =1

`c(n) = (3)(143)^(1-1)` which is not equal to 143.

Hence, it is not the required function.

Let us consider the option B,

`c(n) = 143^(n-1)`

When n=1

c(1) =
`c(n) = 143^(1-1)` = 0, which is not equal to 143.

Hence, it is not the required function.

Let us consider the C option

c(n) = (3)143 − n

When n=1,

c(1) = (3)143 − 1

= 428, which is not equal to 143.

Hence, it is not the required function.

Let us consider the D option

`143(3)^(n-1)`

When n=1

c(1) =
`143(3)^(1-1)`

= 143

Hence, it is the required function.

Therefore, Option D is the correct answer.