Answer:
(1). 110 followers
(2). 463 days
(3). Days since upload 0 10 20 50 100 300 500
Number of Instagram followers 100 122 149 270 732 39158 2,000,000
(5) [tex]f(x)=100(1.03)^d[/tex]
Step-by-step explanation:
Part 1:
The function that represents the situation is:
[tex]f(x) = 100(1 .01)^{2d}[/tex]
Where [tex]d[/tex] is number of days.
Using this equation we find the number of followers after 5 days:
[tex]f(d) = 100(1 .01)^{2*5}=110[/tex] followers.
Part 2:
We solve the equation
[tex]1,000,000 = 100(1 .01)^{2d}[/tex]
for [tex]d[/tex] and get:
[tex]d=463\: days.[/tex]
It takes Alexis 463 days to reach 1,000,000 followers.
Part 3:
Days since upload 0 10 20 50 100 300 500
Number of Instagram followers 100 122 149 270 732 39158 2,000,000
This is obtained from the graph of the function f(x).
Part 4:
The number of Instagram followers increases fast because the rate of increase is 1% of the previous number of followers, and as the followers increase, this 1% takes increasingly big values, leading to increasingly fast growth rate of followers. Put simply, we would say that f(x) is an exponential function.
Par 5:
If the rate is increased to 3% every 24 hours, then the function f(x) becomes:
[tex]f(x)=100(1.03)^d[/tex]
where [tex]d[/tex] is days. and if we represent this in terms of every 12 hours then
[tex]f(x)=100(1.03)^{t/2}[/tex]
where [tex]t[/tex] is every 12 hours.
