Question 424440
The population of a certain endangered species of owl is declining exponentially. There are currently 450 living specimens, whereas just 8 years ago there were 12,000 . If the population continues to decline exponentially, how long will it be until there is only a single owl left?
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apply exponential equation:
y = xe^(kt)
where
y is amount after time t
x is initial amount
k is a constant
t is time
.
plug in all given data to find k:
450 = 12000e^(8k)
450/12000 = e^(8k)
ln(450/12000) = 8k
ln(450/12000)/8 = k
-0.41043 = k
.
Our general equation is:
y = 12000e^(-0.41043t)
.
we now set y to 1 and solve for t:
1 = 12000e^(-0.41043t)
1/12000 = e^(-0.41043t)
ln(1/12000) = -0.41043t
ln(1/12000)/(-0.41043) = t
22.89 years = t