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Answer:
Given,
The initial population ( on 2010 ) = 40,000,
Let r be the rate of increasing population per year,
Thus, the function that shows the population after t years,
And, the population after 5 years ( on 2015 ) is,
According to the question,
P(5) = 50,000,
So, the population is increasing the with rate of 0.04654,
And, the population after t years would be,
Since, the exponential function is,
Hence, by comparing,
a = 40000,
b = 1.04654