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?

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pinquancaro pinquancaro · Answer 1 · 2018-09-07T12:33:05+02:00

The options are:

A. [tex]c(n) = (3)(143)^{n-1}[/tex]

B. [tex]c(n) = 143^{n-1}[/tex]

C. c(n) = (3)143 − n

D.[tex]143(3)^{n-1}[/tex]

SInce, The video of a cat is modeled by the function [tex](3)^{n-1}[/tex]

Let us consider the A option.

[tex]c(n) = (3)(143)^{n-1}[/tex]

When n =1

[tex]c(n) = (3)(143)^{1-1}[/tex] which is not equal to 143.

Hence, it is not the required function.

Let us consider the option B,

[tex]c(n) = 143^{n-1}[/tex]

When n=1

c(1) = [tex]c(n) = 143^{1-1}[/tex] = 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

[tex]143(3)^{n-1}[/tex]

When n=1

c(1) = [tex]143(3)^{1-1}[/tex]

= 143

Hence, it is the required function.

Therefore, Option D is the correct answer.