well, I don't know what "7500 1" means, but I'll just call it 7500 and you can fix it as needed.
For the inverse, swap variables and solve for y:
t = 7500 + 749e^(-0.15y)
t-7500 = 749e^(-0.15y)
e^(-0.15y) = (t-7500)/749
-0.15y = log[(t-7500)/749]
y = -log[(t-7500)/749]/0.15
Clearly, if P is the number of elephants t years after 1903, t is the number of years to arrive at P elephants.
I do not know how to solve for y to get the inverse of 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 1903. Find the inverse of P(t). What is the interpretation of this inverse?
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