Answer:
23.6 years
Explanation:
Given that a population is described by y = 82700e^(-0.00036t), you want to know the value of t when the population is 82000.
Solution
Substitute the given number for y and solve for t:
82000 = 82700e^(-0.00036t)
820/827 = e^-0.00036t . . . . . . . . . . divide by 82700, simplify
ln(820/827) = -0.00036t . . . . . . . . take natural logs
t = ln(820/827)/-0.00036 ≈ 23.6 . . . . . divide by the coefficient of t
It will take approximately 23.6 years.
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Additional comment
The problem statement tells us y₀ is 82700, so we used that in the given equation.
It's a bit odd that the population is reported in thousands of thousands. It could be described as 82.7 million, declinding to 82 million.