Question

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?

Answer 1

Function can be given by , c(n) = $\bold{K4^{n-1}}$, here K is constant

Question said , " on first day , there are 100 likes on video "
Means , put 1 in place of n
e.g., c(1) = 4$\bold{K4^{1-1}} = \bold{K4^0}$ = 100
K = 100

Now, question said " every day 4 times more like on that video "
Means function , c(2) = 4c(1)
c(3) = 4c(2) = 4 × 4c(1) = 4² c(1)
c(4) = 4 × c(3) = 4 × 4 × 4 c(1) = 4³c(1)
..............
...................
c(n) = 4 × 4 × ...... (n -1) times c(1) = 4ⁿ⁻¹ c(1)
But c(1) = K = 100
∴ c(n) = 100 4ⁿ⁻¹

Hence, answer is 100 4ⁿ⁻¹