Exercise 17 Page 210

Let's start with writing the equation in point-slope form and then use it to determine whether the statement is true.

Write the Equation

In order to write the equation in point-slope form, we need to know the slope and a point that solves the equation. We are told that the hot air balloon ascends at a steady rate of 120 feet per minute. Since slope represents a constant rate of change, we can conclude that m= 120. Let's put this into our equation. y-y_1= 120(x-x_1)We are also given that, after 3 minutes of ascending, the balloon is at an altitude of 2330 feet. Let x represent the number of minutes and y represent the number of feet. Substituting 3 for x and 2330 for y, we get the final equation. y- 2330=120(x- 3)

Check the Statement

To determine whether the balloon will reach an altitude of 2500 feet in 4 minutes, we can substitute x with 4 and calculate the actual altitude after 4 minutes of ascending. Then we will compare the result with 2500 and see if the statement is true.

The balloon will be at an altitude of 2450 feet, which is less than 2500. Therefore, it will not reach an altitude of 2500 feet in 4 minutes.