Word Problems Involving Rate Of Change Answer Key Pdf - Fill ... - Free Printable

1. When the dependent variable increases when the independent variable increases, the rate of change is (Positive, Negative, zero, undefined) - Positive
2. When the dependent variable stays the same as the independent variable increases, the rate of change is (Positive, Negative, zero, undefined) - Zero
3. When the dependent variable decreases as the independent variable increases, the rate of change is (Positive, Negative, zero, undefined) - Negative
4. When the dependent variable increases as the independent variable decreases, the rate of change is (Positive, Negative, zero, undefined) - Negative
5. When the dependent variable decreases as the independent variable decreases, the rate of change is (Positive, Negative, zero, undefined) - Positive

Find the rate of change.
6. A climber is at 3000 ft. After 2 hours, he is at an altitude of 4000 ft. After 8 hours, he is at an altitude of 7000 ft. What is the rate of change of his altitude?
- Rate of change = (Change in altitude) / (Change in time)
- From 0 to 2 hours: (4000 - 3000) / (2 - 0) = 1000 / 2 = 500 ft/hour
- From 2 to 8 hours: (7000 - 4000) / (8 - 2) = 3000 / 6 = 500 ft/hour
- The rate of change is constant: 500 ft/hour

7. A scuba diver is 50 feet below the surface of the water 10 seconds after he entered the water and 100 feet below the surface after 40 seconds. What is the scuba diver's rate of change?
- Rate of change = (Change in depth) / (Change in time)
- (100 - 50) / (40 - 10) = 50 / 30 = 5/3 ≈ 1.67 ft/second
- The rate of change is 5/3 ft/second (or approximately 1.67 ft/second)

8. A scuba diver is 2000 feet below sea level. 15 seconds later, he is 2.5 miles below. What is the scuba diver's rate of change in feet per second? What time rate per minute?
- 2.5 miles = 2.5 * 5280 = 13,200 feet
- Change in depth = 13,200 - 2000 = 11,200 feet
- Change in time = 15 seconds
- Rate of change = 11,200 / 15 ≈ 746.67 ft/second
- To find per minute: 746.67 * 60 ≈ 44,800 ft/minute

9. A nuclear scientist is studying uranium with 1000 g of sample. In 2007, 70% of the sample has decayed. What was the rate of change of the sample in grams per year?
- 70% decayed means 30% remains: 0.30 * 1000 = 300 g remaining
- Change in mass = 300 - 1000 = -700 g
- Time = 2007 - 2000 = 7 years
- Rate of change = -700 / 7 = -100 g/year

10. Over the last 30 years, the average temperature has increased by 3.2 degrees worldwide (1 degree fahrenheit). What is the rate of change in worldwide temperature per year?
- Rate of change = 3.2 degrees / 30 years ≈ 0.1067 degrees per year

11. Michael's marathon started with a 5000 ft. elevation. After 4 miles, he had 5350 feet, and after 6 miles, he had 5400. What is the rate of change of elevation in feet per mile?
- From 0 to 4 miles: (5350 - 5000) / 4 = 350 / 4 = 87.5 ft/mile
- From 4 to 6 miles: (5400 - 5350) / 2 = 50 / 2 = 25 ft/mile
- The rate of change is not constant. Average rate over 6 miles: (5400 - 5000) / 6 = 400 / 6 ≈ 66.67 ft/mile

12. A plane had 1500 gallons of fuel. At 1 P.M., the plane landed in Los Angeles, which is 1300 miles away. What was the average speed of the plane for the trip?
- Not enough information to determine speed. We need time. The problem does not provide the time of arrival.

13. After 100 baseball games, Aroldis has 25 hits. After 100 games, he has 80 hits. What is his average hit per baseball game?
- The problem seems to have a typo. If after 100 games he has 25 hits, then after 100 games he has 80 hits? That doesn't make sense. Assuming it's a typo and he has 80 hits after 100 games:
- Average hits per game = 80 / 100 = 0.8 hits per game

Find the slope of a line that has these points.
14. (6,2) and (11,7)
- Slope = (7 - 2) / (11 - 6) = 5 / 5 = 1

15. (5,6) and (4,6)
- Slope = (6 - 6) / (4 - 5) = 0 / (-1) = 0