SOLUTION: Please help!! The growth in the population of a certain rodent at a dump site fits the exponential function, A(t)=336e^(0.031t), where t is the number of years since 1963. Estimat

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Question 151516: Please help!!
The growth in the population of a certain rodent at a dump site fits the exponential function, A(t)=336e^(0.031t), where t is the number of years since 1963. Estimate the population in the year 2000.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, subtract 1963 from 2000 to get 2000-1963=37. So in the year 2000, 37 years have elapsed since 1963. This means that in the year 2000, t=37.


A%28t%29=336e%5E%280.031t%29 Start with the given function.


A%2837%29=336e%5E%280.031%2837%29%29 Plug in t=37


A%2837%29=336e%5E%281.147%29 Multiply 0.031 and 37 to get 1.147


A%2837%29=336%283.14873%29 Raise "e" to the 1.147th power to get 3.14873


A%2837%29=1057.97328 Multiply 336 and 3.14873 to get 1,057.97328


So in the year 2000, there will be approximately 1,058 rats. Note: I rounded to the nearest integer.