SAT Mathematics Practice Test 7

Question : 47 of 59

Marks: +1, -0

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)

$P(t) = 4(1.019)^t$
$P(t) = 4(1.9)^t$
P(t) = 1.19t + 4
P(t) = 1.019t + 4

Validate

Solution:

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 t he world’s population would have been about 4(1.019); in 1977 t he 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.

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