P(t)=2.7(0.9978)t−2019The equation models P, the population of Chicago, in millions, in year t. Which of the following statements is the best interpretation of the ordered pair (2029,2.64) ?Choose 1 answer:(A) The model predicts that the population of Chicago will be increasing at a rate of 2.64 percent in 2029.(B) The model predicts that the population of Chicago will be decreasing at a rate of 2.64 percent in 2029.(C) The model predicts that the population of Chicago will be approximately 2.64 million in 2029.(D) The model predicts that the population of Chicago will increase by approximately 2.64 million in 2029.
Q. P(t)=2.7(0.9978)t−2019The equation models P, the population of Chicago, in millions, in year t. Which of the following statements is the best interpretation of the ordered pair (2029,2.64) ?Choose 1 answer:(A) The model predicts that the population of Chicago will be increasing at a rate of 2.64 percent in 2029.(B) The model predicts that the population of Chicago will be decreasing at a rate of 2.64 percent in 2029.(C) The model predicts that the population of Chicago will be approximately 2.64 million in 2029.(D) The model predicts that the population of Chicago will increase by approximately 2.64 million in 2029.
Plug Year into Model: Plug in the year t=2029 into the model P(t)=2.7(0.9978)(t−2019) to see if the population is approximately 2.64 million.
Calculate t−2019: Calculate t−2019 which is 2029−2019=10.
Substitute into Equation: Substitute 10 into the equation: P(2029)=2.7(0.9978)10.
Calculate Exponential Value: Calculate (0.9978)10 using a calculator.
Multiply by 2.7: The calculation gives approximately 0.9785.
Check Calculation Match: Now multiply 2.7 by 0.9785 to get P(2029).
Predict Population in 2029: The multiplication gives approximately 2.64.
Predict Population in 2029: The multiplication gives approximately 2.64.Since the calculation matches the second value of the ordered pair (2029,2.64), the model predicts that the population of Chicago will be approximately 2.64 million in 2029.
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