Help on how to do this please?
Metro Department Store found that t weeks after the end of a sales promotion the volume of sales was given by
S(t) = B + Ae−kt (0 ≤ t ≤ 4)
where B = 51,000 and is equal to the average weekly volume of sales before the promotion. The sales volumes at the end of the first and third weeks were $81,790 and $62,240, respectively. Assume that the sales volume is decreasing exponentially.
(a) Find the decay constant k. (Round your answer to five decimal places.)
(b) Find the sales volume at the end of the fourth week. (Round your answer to the nearest whole #)

Question

Help on how to do this please?
Metro Department Store found that t weeks after the end of a sales promotion the volume of sales was given by
S(t) = B + Ae−kt      (0 ≤ t ≤ 4)
where B = 51,000 and is equal to the average weekly volume of sales before the promotion. The sales volumes at the end of the first and third weeks were $81,790 and $62,240, respectively. Assume that the sales volume is decreasing exponentially.
(a) Find the decay constant k. (Round your answer to five decimal places.)
(b) Find the sales volume at the end of the fourth week. (Round your answer to the nearest whole #)

vane11 · Answer

I'd like to know the process on how to get the answer, it's for studying purposes since I already turned in the hw assignment for this but I'm pretty sure it's going to be on the test :/

anonymous · Answer

when t =0, S(0) = B = 51000
when t=1 , $S(1) = 51000+ Ae^{-k}=81790\rightarrow Ae^{-k}= 81790-51000=30790$
when t =3, $S(3) =51000+Ae^{-3k}=62240\rightarrow Ae^{-3k}= 11240$
from the 2 equations above, you solve for A and k, that 's the part a)
for part b), just plug A(found out from part a) and t =4