Question

the first recorded population of a particular country was 25 million, and the population was recorded as 29 million 15 years later. the exponential growth function a A=25e^k*t describes the population of this country t years later since the first recording. Use the fact that 15 years later the population increased by 4 million to find k to three decimal places.

Answer 1

To find the value of k in the exponential growth function A = 25e^(kt), with A being 29 million and t being 15 years, we substitute these values into the equation, carry out the necessary steps, and found that k is approximately 0.010.

This question involves using the exponential growth function A = 25e^(kt) to represent the growth of a population from 25 million to 29 million over 15 years, and finding the value of k. We know that A, the population 15 years later, is 29 million, and t, the amount of the time that has passed, is 15 years. By substituting these values into the equation, we get:

29 = 25e^(15k)

Next, we divide both sides of this equation by 25:

29/25 = e^(15k)

To isolate the k, we take the natural of both sides:

ln(29/25) = 15k

So, k = ln(29/25)/15. Calculate this to find that k = 0.010 (rounded to three decimal places).

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