I don't know how to go about this question. The number of elephants in a park is estimated to be
p(t)=7500/(1+749e^-0.15t)
Where t is the time in years and t=0 corresponds to the year 1930. Find the inverse p(t) and the interpretation of that.
since p(t) is the population given time,
p^-1(t) is the time needed to attain a certain population.
p=7500/(1+749e^-0.15t)
1+749e^-0.15t = 7500/p
749e^-0.15t = 7500/p - 1
e^-0.15t = (7500/p - 1)/749
-0.15t = ln((7500/p - 1)/749)
t = -20/3 ln((7500/p - 1)/749)
or
t = -20/3 ln((7500-p)/(749p))
or
t = 20/3 ln((749p)/(7500-p))
or
t = (20 ln749)/3 ln(p/(7500-p))
= 44.125 ln(p/(7500-p))
you can massage the right side to make it prettier if you want.