Explicit Formulas Help!

Question

On June 1, 2019, an instagrammer had 65,000 followers on Instagram. On July 1, 2019 he had 12% more followers than he had in June. With marketing, the Instagrammer wants to continue to increase by 12% each month over the previous month.

A. Find the explicit formula for a sequence of the number of followers he hopes to have each month, starting with

a₁ representing the amount in the first month, June 1, 2019.

B. According to this sequence how many followers will the instagrammer have in January 2021?

Answer 1

Kimberly,

A. The instagrammer starts out with 65,000 followers on June 1st on July 1st he had 12% more so an expression for this would be

Number of followers, N(1)=65,000 +65,000*.12= 65,000*(1+.12)=65,000*(1.12)=72,800.. Ok so far? If we continue with the same calculation for N(2)=72,800*1.12=(65,000*1.12)*1.12 but this is equal to 65,000*(1.12)². Do you see a pattern developing here? The general expression is N(t)= 65,000*(1.12)^t where t is the month number

B. Jan 1 2012 is 20 months out so N(20)=65,000*(1.12)²⁰=65,000*9.65=627,009 followers.

Hope this helps.

Jim

Answer 2

OK. The explicit formula here is not too difficult.

a₂ = a₁ (1 + 0.12)^N

Where a₁ is the 65000 Instagram followers started with. I might even use thousands of followers as my units and let the starting value be 65. a₂ will be the final value.

N is the number of months, since each month there is an increase. July to January is 7.

The final value is 143694 followers, which I would round to 144 thousand.

Answer 3

a_n = 65000(1.12)^(n-1)