Question 143982
a)


{{{P(t)=230 /(1+56.5e^(-.37t)) }}} Start with the given function



{{{P(4)=230 /(1+56.5e^(-.37(4))) }}} Plug in {{{t=4}}}



{{{P(4)=230 /(1+56.5e^(-1.48)) }}} Multiply -.37 and 4 to get -1.48



{{{P(4)=230 /(1+56.5(0.22764)) }}} Raise e to the -1.48 to get 0.22764



{{{P(4)=230 /(1+12.86166) }}} Multiply 56.5 and 0.22764 to get 12.86166



{{{P(4)=230 /(13.86166) }}} Add 1 and 12.86166 to get 13.86166 



{{{P(4)=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)




<hr>



b)



{{{P(t)=230 /(1+56.5e^(-.37t)) }}} Start with the given function



{{{P(0)=230 /(1+56.5e^(-.37(0))) }}} Plug in {{{t=0}}}



{{{P(0)=230 /(1+56.5e^(0)) }}} Multiply -.37 and 0 to get 0



{{{P(0)=230 /(1+56.5(1)) }}} Raise e to the zeroth power to get 1



{{{P(0)=230 /(1+56.5) }}} Multiply 56.5 and 1 to get 56.5



{{{P(0)=230 /(57.5) }}} Add 1 and 56.5 to get 57.5 



{{{P(0)=4 }}} Divide 57.5 into 230 to get 4




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