The function given to us is:
[tex] V(t) = 580(1.17)^t [/tex]
where [tex] t [/tex] is in days.
We know that the number of days in a week is 7.
Thus, to find out by what factor does the number of views grow in a week all that we have to do is realize that the starting of any week will have the expression as:
[tex] V(t) = 580(1.17)^t [/tex]..................(Equation 1)
and the end of the week will have the expression as:
[tex] V(t+7) = 580(1.17)^{t+7} [/tex]..................(Equation 2)
And so to find the growth factor in a week, we will have to divide (Equation 2) by (Equation 1), which yields:
[tex] \frac{V(t+7)}{V(t)}=\frac{580(1.17)^{t+7}}{580(1.17)^{t}}=\frac{(1.17)^t\times (1.17)^7}{(1.17)^t} [/tex]
[tex] \therefore \frac{V(t+7)}{V(t)}=(1.17)^7\approx3 [/tex]
Thus, the number of views grow by a factor of 3 in a week.
