Mathematics

Question

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 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

  • 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]

    Step-by-step 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]

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