Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

P(t)=2.7(0.9978)^(t-2019)
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) ?
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.

P(t)=2.7(0.9978)t2019 P(t)=2.7(0.9978)^{t-2019} \newlineThe equation models P P , the population of Chicago, in millions, in year t t . Which of the following statements is the best interpretation of the ordered pair (2029,2.64) (2029,2.64) ?\newlineChoose 11 answer:\newline(A) The model predicts that the population of Chicago will be increasing at a rate of 22.6464 percent in 20292029.\newline(B) The model predicts that the population of Chicago will be decreasing at a rate of 22.6464 percent in 20292029.\newline(C) The model predicts that the population of Chicago will be approximately 22.6464 million in 20292029.\newline(D) The model predicts that the population of Chicago will increase by approximately 22.6464 million in 20292029.

Full solution

Q. P(t)=2.7(0.9978)t2019 P(t)=2.7(0.9978)^{t-2019} \newlineThe equation models P P , the population of Chicago, in millions, in year t t . Which of the following statements is the best interpretation of the ordered pair (2029,2.64) (2029,2.64) ?\newlineChoose 11 answer:\newline(A) The model predicts that the population of Chicago will be increasing at a rate of 22.6464 percent in 20292029.\newline(B) The model predicts that the population of Chicago will be decreasing at a rate of 22.6464 percent in 20292029.\newline(C) The model predicts that the population of Chicago will be approximately 22.6464 million in 20292029.\newline(D) The model predicts that the population of Chicago will increase by approximately 22.6464 million in 20292029.
  1. Plug Year into Model: Plug in the year t=2029t = 2029 into the model P(t)=2.7(0.9978)(t2019)P(t)=2.7(0.9978)^{(t-2019)} to see if the population is approximately 2.642.64 million.
  2. Calculate t2019t-2019: Calculate t2019t-2019 which is 20292019=102029-2019 = 10.
  3. Substitute into Equation: Substitute 1010 into the equation: P(2029)=2.7(0.9978)10P(2029)=2.7(0.9978)^{10}.
  4. Calculate Exponential Value: Calculate (0.9978)10(0.9978)^{10} using a calculator.
  5. Multiply by 22.77: The calculation gives approximately 0.97850.9785.
  6. Check Calculation Match: Now multiply 2.72.7 by 0.97850.9785 to get P(2029)P(2029).
  7. Predict Population in 20292029: The multiplication gives approximately 2.642.64.
  8. Predict Population in 20292029: The multiplication gives approximately 2.642.64.Since the calculation matches the second value of the ordered pair (2029,2.64)(2029,2.64), the model predicts that the population of Chicago will be approximately 2.642.64 million in 20292029.

More problems from Solve quadratic equations: word problems