Question

100 POINTS!!!!

Answer 1

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:

$t= 462.82\ days$

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

$\displaystyle f(x) = f_o(1 + r)^t$

Where $f_o$ 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:

$\displaystyle f(x) = 100(1.01)^t$

We need to know when the number of followers will reach 1,000,000. Setting up the equation

$\displaystyle 100(1.01)^t=1,000,000$

Simplifying by 100

$\displaystyle (1.01)^t=10,000$

Taking logarithms

$\displaystyle t\ log(1.01)=log\ 10,000$

$\displaystyle t\ log(1.01)=4$

Solving for t

$\displaystyle t=\frac{4}{log(1.01)}=925.63$ periods of 12 hrs

$t= 462.82\ days$