100 POINTS!!!! Alexis runs a small business and creates recordings of her friend’s skateboard stunts. She puts the recordings onto Instagram. She currently has
Question
Alexis runs a small business and creates recordings of her friend’s skateboard stunts. She puts the recordings onto Instagram. She currently has 100 Instagram followers. If the number of followers grows at a rate of 1% every 12 hours. The following function represents this situation.
f(x) = f(1. + r)^t where f is the number of initial followers and r is the grown rate and t is time.
2) Alexis hopes to eventually have 1,000,000 followers, how long will it take her to reach this level of followers.
#Days since upload 0 10 20 50 100 300 500
Number of Instagram followers
1 Answer

1. User Answers elcharly64
There is no specific requirement in the question, but I'm assuming you need to compute the time needed for Alexis reach 1,000,000 Instagram followers
Answer:
[tex]t= 462.82\ days[/tex]
Stepbystep explanation:
Exponential Growth
When the number of observed elements grows as the previous value multiplied by a constant ratio, we have exponential growth. The formula to model such situations is
[tex]\displaystyle f(x) = f_o(1 + r)^t[/tex]
Where [tex]f_o[/tex] is the initial value of f, 1 + r is the constant ratio, and t is the time expressed in half days (12 hours)
The initial value is 100 Instant followers, thus:
[tex]\displaystyle f(x) = 100(1.01)^t[/tex]
We need to know when the number of followers will reach 1,000,000. Setting up the equation
[tex]\displaystyle 100(1.01)^t=1,000,000[/tex]
Simplifying by 100
[tex]\displaystyle (1.01)^t=10,000[/tex]
Taking logarithms
[tex]\displaystyle t\ log(1.01)=log\ 10,000[/tex]
[tex]\displaystyle t\ log(1.01)=4[/tex]
Solving for t
[tex]\displaystyle t=\frac{4}{log(1.01)}=925.63[/tex] periods of 12 hrs
[tex]t= 462.82\ days[/tex]