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The population of a town is currently 9,000. The function p = 9,000 + 8t can be used to estimate p, the population of the town t years from now. Which statement about this function is true?

A. The population of the town is increasing at a constant rate.

B. The population of the town will reach 10,000 between 11 and 12 years from now.

C. The population of the town will increase by 256 people two years from now.

D. The population of the town will increase and then decrease.

User Plan
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1 Answer

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Final answer:

The true statement about the function p = 9,000 + 8t is A, the population of the town is increasing at a constant rate. Statements B, C, and D are false based on the analysis of the function.

Step-by-step explanation:

The question relates to the function p = 9,000 + 8t, which models the population growth of a town over time. We can analyze each statement to determine which is true.

A. The function shows a constant rate of increase for the population since the number of people added each year is constant, which is indicated by the +8t term.

B. To find when the population reaches 10,000, we can set up an equation: p = 10,000 = 9,000 + 8t. Solving for t yields t = 125, which is not between 11 and 12 years, so this statement is false.

C. To determine the population increase two years from now, we substitute t=2 into the function. p = 9,000 + 8(2) = 9,016, so the population will increase by 16 people, not 256, making this statement false.

D. Since there is no term in the function to reflect a decrease, the population is modeled to only increase, without any decrease over time. Thereby, this statement is also false.

User Nnyby
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