Question

The populations of two cities after t years can be modeled by -400t + 225,000 and 750t + 115,000. What is the difference in the populations of the cities when t = 3?

Answer 1

To find the difference in populations of two cities after 3 years given their population models, we plug in t = 3 into both equations and subtract the second city's population from the first, resulting in a difference of 106,550.

Step-by-step explanation:

The question asks for the difference in the populations of two cities after t years, given their population models as -400t + 225,000 and 750t + 115,000. To find the difference in populations when t = 3, we need to plug in t = 3 into both equations and subtract the second result from the first.

1. Calculate the population of the first city after 3 years: -400(3) + 225,000 = -1,200 + 225,000 = 223,800.
2. Calculate the population of the second city after 3 years: 750(3) + 115,000 = 2,250 + 115,000 = 117,250.
3. Find the difference between the two populations: 223,800 - 117,250 = 106,550.

Therefore, the difference in the populations of the two cities when t = 3 is 106,550.