Question 593293
The exponential growth function is 


{{{N(t) = N[0]*e^(kt)}}} where N(t) is the population at time t, {{{N[0]}}} is the initial population and k is the growth constant (some positive number in the interval [0,1])



In this case, the initial population is 200, so {{{N[0]=200}}}


So the function {{{N(t) = N[0]*e^(kt)}}} then becomes {{{N(t) = 200*e^(kt)}}}


The growth rate is 11.7% per day, so when {{{t=1}}}, the population is now 200 + 0.117*200 = 223.4


So this means we have the equation 


{{{223.4 = 200*e^(k)}}}



Let's solve for k



{{{223.4 = 200*e^(k)}}}


{{{223.4/200 = e^(k)}}}


{{{1.117 = e^(k)}}}


{{{ln(1.117) = ln(e^(k))}}}


{{{ln(1.117) = k*ln(e)}}}


{{{ln(1.117) = k*(1)}}}


{{{ln(1.117) = k}}}


{{{0.110646520087064 = k}}}


{{{k = 0.110646520087064}}}


So the growth constant is approximately {{{k = 0.110647}}}



Therefore, the exponential growth function is 



{{{N(t) = 200e^(0.110647t)}}}