Question

5.7 pts. In January 2019, an influencer had 4,000 followers. In July 2019, they had 10,000 followers. A. Assuming an exponential model for the growing number of followers, find the growth constant k. Round your answer for k to 4 decimal places. B. Find the exponential growth function N(t) which gives the number of followers after t months. Make sure you plug in all the constants you have for the function, such as N(0) and k. C. How many followers does this model predict there will be in January 2020? (Round your answer to the nearest follower.) D. If the follower population continues to grow according to this model, when will this influencer have 100,000 followers?

Answer 1

t = akt Graven Sh January 2014 , influencere had 4,000 Followers In July 2019, they had 20000 followers SH we take January 2014 as ential state Then the exponential model for this problem 28 N(t) = akt where NCA) = numbere of followere oftere t months a = NO andand number of followere at anatoal state K= growth constant @ Now Ala, at Januar 2019 ze t=0 N(O)= aho = a = 4.000 and N at July 2019 ze t = 6 N(6)= 10000 =) a ek = 10000 = yooo. eK = 10000 - e6k - 1000 -) 6K – en - K= I en = K = 0.1527.

Now N(A) = a ekt - 4ooo. et en). t = 4000. en = 4000.0() = N(H) = 4000 (z lt cohere te number of followere oftere + marths of January 2019 C) At January 2020 m t= 12 so numbere of follower at January 2020 25 N (42) = 4000 x ( =4000 x 612 -4000x 28 = 25000 (d) ozven N(t)= 100000 => 4000 () = 100000 -) (3)& __ 100000 = 25 - t ens = enas 6lna - 21.077 221 After 21 moths after Tanuary 2019 ze ozn september 2020 the populatan of followere growrs to 100000 - t = n =