SOLUTION: Annual sales S for a particular product t years after it is introduced is given by the function S=2000/1+4e^-t/2. When will sales reach 1100 units per year?

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Question 551355: Annual sales S for a particular product t years after it is introduced is given by the function S=2000/1+4e^-t/2. When will sales reach 1100 units per year?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Annual sales S for a particular product t years after it is introduced is given by the function S=2000/1+4e^-t/2. When will sales reach 1100 units per year?
:
Assume the equation is:
S=2000%2F%28%281%2B4e%5E%28-t%2F2%29%29%29
:
1100 = 2000%2F%28%281%2B4e%5E%28-t%2F2%29%29%29
:
1100%281%2B4e%5E%28-t%2F2%29%29 = 2000
:
%281%2B4e%5E%28-t%2F2%29%29 = 2000%2F1100
:
%281%2B4e%5E%28-t%2F2%29%29 = 1.8182
:
%284e%5E%28-t%2F2%29%29 = 1.8182 - 1
:
%284e%5E%28-t%2F2%29%29 = .8182
:
%28e%5E%28-t%2F2%29%29 = .8182%2F4
:
%28e%5E%28-t%2F2%29%29 = .2045
:
ln%28e%5E%28-t%2F2%29%29 = ln(.2045)
-t%2F2 = -1.587; the nat log of e = 1
t = -1.587 * -2
t = +3.174 yrs; for sales to reach 1100 units