SOLUTION: A house has been infested with termites, and the infestation is represented by the growth function, f(t)=55001+30e−0.5t, which describes the number of termites present t day

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: A house has been infested with termites, and the infestation is represented by the growth function, f(t)=55001+30e−0.5t, which describes the number of termites present t day      Log On


   

Question 1043638: A house has been infested with termites, and the infestation is represented by the growth function, f(t)=55001+30e−0.5t, which describes the number of termites present t days after the initial outbreak.
Find the following:
A) Find the number of termites present at the initial outbreak. (Round your answer to the nearest whole number.)
Answer = approximately termites
B) Find the termite population after 8 days. (Round your answer to the nearest whole number.)
Answer = approximately termites

Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
The growth function is
f%28t%29+=+55001%2B+30%2Ae%5E%28-0.5t%29
This describes the number of termites present t days after the initial outbreak.
f%28t%29+=+55001%2B+30%2Ae%5E%28-0.5t%29
now solve for t=0
f%28t=0%29+=+55001%2B+30%2Ae%5E%28-0.5%2A0%29
which gives
f%28t=0%29+=+55001%2B+30=55031
now solve for t=8
f%28t=8%29+=+55001%2B+30%2Ae%5E%28-0.5%2A8%29=55019.1959198
rounded to the nearest whole number=55019
i hope i am correct because it looks like decay the - makes it look like decay.