The population of a town with a 20162016 population of 87 comma 00087,000 grows at a rate of 1.91.9% per year. a. find the rate constant k and use it to devise an exponential growth function that fits the given data. b. in what year will the population reach 145 comma 000145,000?

Given,

The initial population, P = 87,000,

Annual rate of increasing, r = 1.9 %,

a) Thus, the population after t years,

Where, k is the rate constant,

By comparing,

Hence, the approximate value of k is 0.00817.

And, the exponential growth function would be,

b) If A = 145,000,

By using graphing calculator,

We get,

The year after 27 years from 2016 is 2043.

Hence, in 2043 the population reach 145,000.

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problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

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