Question

10) The population of a particular country was 29 million in 1980; in 1985, it was 38 million. The exponential

growth function A = 29e^kt describes the population of this country t years after 1980. Use the fact that 5
after 1980 the population increased by 9 million to find k to three decimal places.
years

Answer 1

Answer: To three decimal places, k ≈ 0.052.

Step-by-step explanation: We are given the exponential growth function A = 29e^kt, where A is the population in millions t years after 1980.

In 1980, the population was 29 million, so A = 29 when t = 0. Substituting these values into the equation, we get:

29 = 29e^k(0)

29 = 29e^0

29 = 29

This confirms that the equation is true for t = 0.

In 1985, the population was 38 million, so A = 38 when t = 5. Substituting these values into the equation, we get:

38 = 29e^k(5)

Dividing both sides by 29, we get:

38/29 = e^5k

Taking the natural logarithm of both sides, we get:

ln(38/29) = 5k

Solving for k, we get:

k = ln(38/29) / 5 ≈ 0.052

Therefore, to three decimal places, k ≈ 0.052.