Question 980288
You should find that c = 58500 and b = 116.



{{{p(t) = c/(1+Be^(k*t))}}}



{{{p(t) = 58500/(1+116e^(k*t))}}} Plug in c = 58500 and b = 116



{{{20500 = 58500/(1+116e^(k*3))}}} Plug in t = 3 and p(t) = 20500 (since 3 years after 1995, the amount of runners is 20500)



{{{20500(1+116e^(k*3)) = 58500}}}



{{{20500+2378000e^(3k) = 58500}}}



{{{2378000e^(3k) = 58500-20500}}}



{{{2378000e^(3k) = 38000}}}



{{{e^(3k) = 38000/2378000}}}



{{{e^(3k) = 0.01597981497057}}}



{{{3k = ln(0.01597981497057)}}}



{{{3k = -4.1364289175233}}}



{{{k = -4.1364289175233/3}}}



{{{k = -1.37880963917443}}}



{{{k = -1.3788}}} (rounding to 4 decimal places)



So the function is {{{p(t) = 58500/(1+116e^(-1.3788t))}}}