Hi guys, I need help finding A in this equation so that I can go ahead and answer the actual questions (not included) can someone help me?

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.

Question

Hi guys, I need help finding A in this equation so that I can go ahead and answer the actual questions (not included) can someone help me?

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.

campbell_st · Answer

so the equation is 

$$S(t) = B + Ae^{-kt}$$

vane11 · Answer

yes sorry

campbell_st · Answer

ok... look at week 1 of the promotion 

$$81790 = 51000 +Ae^{-k}$$

or 

$$30790 = Ae^{-k}$$

and in week 3

$$62240 = 51000 + A e^{-3k}$$

or 

$$10240 = Ae^{-3k}$$

so I would split the week 3 equation to 

$$10240 = Ae^{-k} \times e^{-2k}$$

then substitute the week 1 simplified equation. 

this will allow you to solve for k... 

then when you have k, you can find A

hope it helps

vane11 · Answer

ohhhh ok, thanks!