Question

The number of a certain species of fish is modeled by the function:

n(t) = 12e^{0.012t} ,

where t is measured in years and n(t) is measured in millions.

c) After how many years will the number of fish reach 30 million?

This is the answer I got, but for some reason, it doesn't really make sense to me:

SOLN:
To find when the fish pop'n will reach 30mil., sub in '30' for n(t) and solve for 't'.
30 = 12*e^{0.012t}
30/12 = e^{0.012t}
5/2 = e^{0.012t}
Take the ln of both sides

ln(5/2) = ln(e^{0.012t})
ln(5/2) = 0.012t
ln(5/2) / 0.012 = t
76/35 = t

Therefore, after about 76.4 years, the...

Answer 1

.. the fish population will reach 30 million. Is this correct?

Answer 2

looks good