Answer: [tex]y=98(2)^{4t}[/tex]
Step-by-step explanation:
The exponential growth function is given by :_
[tex]y=A(b)^x[/tex], where A is the initial amount , b is the multiplicative growth rate and x is the time period.
Given : The number of visitors, V, a website receives doubles every 3 months.
i.e. The growth factor for every 3 months : b= 2
For 6 months , the number of time period = [tex]x=\dfrac{6}{3}=2[/tex]
If 6 months ago the website received 24,500 visitors, then the number of visitors now :-
[tex]y=24500(2)^2=98000[/tex]
Time periods for 1 year = [tex]\dfrac{12}{3}=4[/tex]
Then, time periods for increase in t-years= [tex]4t[/tex]
For now, the initial number of visitors ( in thousand)= [tex]A_1=98[/tex]
Then, the function of the number of visitors (in thousand) website receive in t years:-
[tex]y=98(2)^{4t}[/tex]
