SOLUTION: Please help! :( How would I solve the below problem? And what is the final answer? A scientist determined that the fruit fly population for his experiment is given by the equat

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Question 143982: Please help! :( How would I solve the below problem? And what is the final answer?
A scientist determined that the fruit fly population for his experiment is given by the equation: P(t)= 230 / 1+56.5e(exponent)-.37t where P(t) is the population of the fruit flies after t days.
(a) Find the number of fruit flies after 4 days
(b) What was the number of fruit flies at the beginning of the experiment.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)

P%28t%29=230+%2F%281%2B56.5e%5E%28-.37t%29%29+ Start with the given function


P%284%29=230+%2F%281%2B56.5e%5E%28-.37%284%29%29%29+ Plug in t=4


P%284%29=230+%2F%281%2B56.5e%5E%28-1.48%29%29+ Multiply -.37 and 4 to get -1.48


P%284%29=230+%2F%281%2B56.5%280.22764%29%29+ Raise e to the -1.48 to get 0.22764


P%284%29=230+%2F%281%2B12.86166%29+ Multiply 56.5 and 0.22764 to get 12.86166


P%284%29=230+%2F%2813.86166%29+ Add 1 and 12.86166 to get 13.86166


P%284%29=16.59253+ Divide 13.86166 into 230 to get 16.59253


So after 4 days, there are about 17 flies (I rounded to the nearest whole number)






b)


P%28t%29=230+%2F%281%2B56.5e%5E%28-.37t%29%29+ Start with the given function


P%280%29=230+%2F%281%2B56.5e%5E%28-.37%280%29%29%29+ Plug in t=0


P%280%29=230+%2F%281%2B56.5e%5E%280%29%29+ Multiply -.37 and 0 to get 0


P%280%29=230+%2F%281%2B56.5%281%29%29+ Raise e to the zeroth power to get 1


P%280%29=230+%2F%281%2B56.5%29+ Multiply 56.5 and 1 to get 56.5


P%280%29=230+%2F%2857.5%29+ Add 1 and 56.5 to get 57.5


P%280%29=4+ Divide 57.5 into 230 to get 4



So at the beginning of the experiment, there are 4 flies.