Question

1. braden is hiking on a mountain. at 11:00 a.m., he is at an elevation of 500 feet. at 2:00 p.m., he is at 900 feet. find the rate of change in elevation.
2. a car worth $2 in 2016. find t value of the c
3. in math class, blake earned a 94 in the first quarter, an 86 in the second quarter, an 88 in the third quarter, and a 96 in the fourth quarter. find the rate of change from the second to the fourth quarter.
4. the boston p 2004 seaso 748 runs. fi
5. kayla consumed 1800 calories on monday. she consumed 300 more calories on tuesday than she did on monday. on wednesday, she consumed 100 calories less than she had on tuesday. find the rate of change in calories intake from monday to wednesday
6. drew me during c inches h 3 feet h change

Explanation:

Problem 13:

Step1: Determine time change

From 11:00 a.m. to 2:00 p.m., the time elapsed is \(2 - 11 + 12 = 3\) hours (or directly calculate \(14 - 11 = 3\) hours, since 2:00 p.m. is 14:00 in 24 - hour time).

Step2: Determine elevation change

The elevation changes from 500 feet to 900 feet, so the change in elevation is \(900 - 500 = 400\) feet.

Step3: Calculate rate of change

The rate of change (slope) is given by \(\frac{\text{change in elevation}}{\text{change in time}}\), so \(\frac{400}{3}\approx133.33\) feet per hour.

Step1: Determine quarter change

From the second to the fourth quarter, the number of quarters elapsed is \(4 - 2 = 2\) quarters.

Step2: Determine grade change

The grade changes from 86 to 96, so the change in grade is \(96 - 86 = 10\).

Step3: Calculate rate of change

The rate of change is \(\frac{\text{change in grade}}{\text{change in quarter}}\), so \(\frac{10}{2}=5\) per quarter.

Step1: Find Tuesday's calories

Kayla consumed 1800 calories on Monday. On Tuesday, she consumed \(1800 + 300 = 2100\) calories.

Step2: Find Wednesday's calories

On Wednesday, she consumed \(2100 - 100 = 2000\) calories.

Step3: Determine day change and calorie change

From Monday to Wednesday, the number of days elapsed is \(3 - 1 = 2\) days. The change in calories is \(2000 - 1800 = 200\) calories.

Step4: Calculate rate of change

The rate of change is \(\frac{200}{2}=100\) calories per day.

Answer:

The rate of change in elevation is \(\frac{400}{3}\) (or approximately \(133.33\)) feet per hour.

Problem 15: