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.
1) Alexis wants to figure out how many followers she will have after 5 days, use the equation to solve.

2) Alexis hopes to eventually have 1,000,000 followers, how long will it take her to reach this level of followers.

3) Fill in the chart below.


#Days since upload 0 10 20 50 100 300 500

Number of Instagram followers
4) In words, explain why the rate increases so fast.

5) Create an equation for the number of followers if the rate increased 3% every 24 hours.

Answer 1

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) $f(x)=100(1.03)^d$

Step-by-step explanation:

Part 1:

The function that represents the situation is:

$f(x) = 100(1 .01)^{2d}$

Where $d$ is number of days.

Using this equation we find the number of followers after 5 days:

$f(d) = 100(1 .01)^{2*5}=110$ followers.

Part 2:

We solve the equation

$1,000,000 = 100(1 .01)^{2d}$

for $d$ and get:

$d=463\: days.$

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:

$f(x)=100(1.03)^d$

where $d$ is days. and if we represent this in terms of every 12 hours then

$f(x)=100(1.03)^{t/2}$

where $t$ is every 12 hours.