$P(t)=2.7(0.9978)^{t-2019}$ $\newline$ The 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 $(2029,2.64)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) The model predicts that the population of Chicago will be increasing at a rate of $2$ . $64$ percent in $2029$ . $\newline$ (B) The model predicts that the population of Chicago will be decreasing at a rate of $2$ . $64$ percent in $2029$ . $\newline$ (C) The model predicts that the population of Chicago will be approximately $2$ . $64$ million in $2029$ . $\newline$ (D) The model predicts that the population of Chicago will increase by approximately $2$ . $64$ million in $2029$ .

Full solution

P(t)=2.7(0.9978)^{t-2019}

\newline

The 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)

\newline

Choose

1

answer:

\newline

(A) The model predicts that the population of Chicago will be increasing at a rate of

2

64

percent in

2029

\newline

(B) The model predicts that the population of Chicago will be decreasing at a rate of

2

64

percent in

2029

\newline

2

64

million in

2029

\newline

(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 $2029$ .