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The world’s population has grown at an a...

The world’s population has grown at an average rate of 1.9 percent per year since 1945. There were approximately 4 billion people in the world in 1975. Which of the following functions represents the world’s population P, in billions of people, t years since 1975 ? (1 billion = 1,000,000,000)

A

`P(t) = 4(1.019)^t`

B

`P(t) = 4(1.9)^t`

C

P(t) = 1.19t + 4

D

P(t) = 1.019t + 4

Text Solution

Verified by Experts

The correct Answer is:
A
Because the world’s population has grown at an average rate of 1.9% per year since 1945, it follows that the world’s population has been growing by a constant factor of 1.019 since 1945. If the world’s population in 1975 was about 4 billion, in 1976 the world’s population would have been about 4(1.019), in 1977 the world’s population would have been about 4(1.019)(1.019), or `4(1.019)^2`, and so forth. Therefore, the world’s population, P(t), t years since 1975 could be represented by the function `P(t) = 4(1.019)^t`. Choice B is incorrect because it represents a 90% increase in population each year. Choices C and D are incorrect because they are linear models, which represent situations that have a constant growth.
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