Multiple choice

g(x) = 30.5(1.08)x The population of a certain species of birds, in thousands, from the years 2000 to 2020 can be modeled by the function g, where x is the number of years after 2000. Which of the following is the best interpretation of the number 1.08 in this context?

  1. On average, the population increased by approximately 0.08 thousand birds per year.

  2. On average, the population increased by approximately 1.08 thousand birds per year.

  3. On average, the population increased by approximately 8% per year.

  4. On average, the population increased by approximately 108% per year.
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C Correct answer
Explanation

In the exponential growth model g(x) = a(b)^x, the base b represents (1 + r), where r is the growth rate. Here, 1.08 = 1 + 0.08, which corresponds to an 8% increase per year.

AI explanation

The function g(x) = 30.5(1.08)^x represents exponential growth, where the base, 1.08, is the growth factor. In an exponential growth model, a base of 1 plus a decimal indicates a percentage increase equal to that decimal multiplied by 100. Therefore, 1.08 signifies an 8 percent annual increase in the bird population. The result is that the population increased by approximately 8% per year.

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