SOLUTION: Two parter that I don't understand. Can anyone help me? The black bear population in a certain are in Alaska is approximated by B(t) = 580/1 + 8.3e^-0.12t, t is the nu

Question 64439: Two parter that I don't understand. Can anyone help me?
The black bear population in a certain are in Alaska is approximated by
B(t) = 580/1 + 8.3e^-0.12t,
t is the number of years after logging ended in the area. How many black bearsare there 5 years after logging ended? Predict how long it will take for the black bear population to reach 290.
Thanks again.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The black bear population in a certain are in Alaska is approximated by
B(t) = 580/1 + 8.3e^-0.12t,
t is the number of years after logging ended in the area. How many black bears are there 5 years after logging ended? Predict how long it will take for the black bear population to reach 290.
Comment: Your formula is ambiguous. It is difficult to tell where
the denominator starts and where it ends. I'm going to assume 1+8.3e^-0.12t
is all in the denominator.

B(t) = 580/[1 + 8.3e^-0.12t]
B(5)=580/[1+8.3e^(-0.12*5)
B(5)=580/5.55513658
B(5)=104.4 bears
---------------
If B(t)=290 find "t".
290=580/(1+8.3e^(-0.12t)
1+8.3e^(-0.12t)=580/290=2
8.3e^(-0.12t)=1
e^(-0.12t)=0.1204819277...
Take the natural log of both sides to get:
-0.12t=-2.11625555...
t=17.635 years
Cheers,
Stan H.
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