Solve the problem.
-The population of a particular country was 24 million in 1980; in 1994, it was 32 million. The exponential growth function describes the population of this country t years after 1980. Use the fact that 14 years
After 1980 the population increased by 8 million. Find k rounded to three decimal places.
A) 0.475
B) 0.149
C) 0.021
D) 0.031

Question

Solve the problem.
-The population of a particular country was 24 million in 1980; in 1994, it was 32 million. The exponential growth function  describes the population of this country t years after 1980. Use the fact that 14 years
After 1980 the population increased by 8 million. Find k rounded to three decimal places.
A) 0.475 
B) 0.149 
C) 0.021 
D) 0.031

Quizplus · Accepted Answer

Using the given information, we know that:

1980 population = 24 million
1994 population = 32 million
Population increased by 8 million in 14 years.

Using the exponential growth function:

32 = 24e^(k*14)

Solving for k:

ln(32/24) = k*14
ln(4/3) = 14k
k = ln(4/3)/14 ≈ 0.021

Therefore, the answer is C) 0.021. We can use the information given to set up two equations:

11ebb63d_1bdc_13f4_b851_154841fca473_TB8475_12  = 24e^k(0) = 24
11ebb63d_1bdc_13f4_b851_154841fca473_TB8475_13  = 32e^k(14)

We want to find k such that the population increased by 8 million over 14 years. That means:

32e^k(14) - 24e^k(0) = 8
e^14k = 1.33333...
14k ≈ ln(1.33333...)
k ≈ 0.0205

Rounded to three decimal places, the answer is 0.021. Therefore, the answer is C.

Solve the Problem. -The Population of a Particular Country Was 24 Million in 24