Growth model word problem w/differential equations
Biology. A population of eight beavers has been introduced into a new wetlands area. Biologists estimate that the maximum population the wetlands can sustain is 60 beavers. After 3 years, the population is 15 beavers. If the population follows a Gompertz growth model, how many beavers will be in the wetlands after 10 years?
Gompertz growth model:
Here's what I did.
My values for the variables are:
However, the solutions manual states the answer for the general soln is
which is a difference of signs for the constant in the exponential. I'm not sure where I went wrong but I don't want to start plugging in values until I have the right general solution. Help please? :)