Every day, there are 4 times more likes on an internet video of a horse which is modeled by the function c(n) = (4)n − 1, where n is the number of days since the video posted. On the first day, there were 100 likes. What is the function that shows the number of likes each day?

A better way to write the first function would be:
c(n) = 4 * c(n-1), meaning that the number of of likes is equal to four times the number of likes from the previous day. 
On the first day, c(n), or c(0) = 100
Therefore:
C(n) = 100 * 4^n 
Let's plug in a view values to test our function: 
When n= 0 (first day)
C(0) = 100 * 4 ^0 = 100*1 = 100 likes
C(1) = 100 * 4^1 = 100 * 4 = 400 likes, four times the previous day
C(2) = 100 * 4^2 = 100 * 16 = 1600 likes, four times the previous day
And so on. Our function is an accurate descriptor of the model.