Question 1. A squirrel has stored its acorns in a hole that is 45 feet from the ground in a tall tree. The squirrel starts on a perch 100 feet above the ground. The squirrel moves from the perch down to its stored acorns in 5.25 seconds. Interpret the quotient to describe the rate of change in the squirrel’s height above the ground. Give your answer to the nearest hundredth.
Question 2. A dolphin jumped above the surface of the water. It reached an altitude of 3.5 meters above the surface of the water and then dove 10 meters below the surface of the water. It went from its highest point above the water to its lowest depth in 12.5 seconds. Interpret the quotient to describe the average rate of change in the dolphin’s position. Give your answer to the nearest hundredth.
Question 3. A scuba diver was at a depth of 15 meters below the surface when she saw something interesting about 10 meters lower. She made the descent in 10.1 seconds. Interpret the quotient to describe the rate of change in the diver’s depth. Give your answer to the nearest hundredth.
Question 4. Solve using division of rational numbers. If a car’s value decreases by $4,000 in the first 12 months, how much does the value decrease per month? (Round to the nearest hundredth.)
Question 5. It is recommended that hikers drink 24 ounces of water an hour. If a canteen has 24 ounces of water, how much should the amount of water in the canteen change every 10 minutes?
Question 1: The quotient is 8.57. This means that the squirrel's height above the ground decreased at a rate of approximately 8.57 feet per second.
Question 2: The quotient is -0.80. This means that the dolphin's position changed at an average rate of approximately -0.80 meters per second.
Question 3: The quotient is -0.99. This means that the diver's depth decreased at a rate of approximately 0.99 meters per second.
Question 4: The quotient is -333.33. This means that the car's value decreased by approximately $333.33 per month.
Question 5: The quotient is -2.40. This means that the amount of water in the canteen should decrease by approximately 2.40 ounces every 10 minutes.
Can you explain the process of all the questions?
Sure! Let's go through each question step by step:
Question 1:
To find the rate of change in the squirrel's height above the ground, we divide the change in height (45 feet) by the time it took to make that change (5.25 seconds). So the quotient is 45/5.25, which is approximately 8.57. We interpret this as the squirrel's height above the ground decreasing at a rate of approximately 8.57 feet per second.
Question 2:
To find the average rate of change in the dolphin's position, we divide the change in position (10 meters) by the time it took to make that change (12.5 seconds). So the quotient is 10/12.5, which is approximately 0.80. However, since the dolphin dove below the surface, we consider the change in position as negative. Therefore, the average rate of change is approximately -0.80 meters per second.
Question 3:
To find the rate of change in the diver's depth, we divide the change in depth (10 meters) by the time it took to make that change (10.1 seconds). So the quotient is 10/10.1, which is approximately 0.99. However, since the diver went deeper, we consider the change in depth as negative. Therefore, the rate of change is approximately -0.99 meters per second.
Question 4:
To find how much the car's value decreases per month, we divide the decrease in value ($4,000) by the number of months (12). So the quotient is 4,000/12, which is approximately 333.33. However, since the value is decreasing, we consider it as negative. Therefore, the value decreases by approximately $333.33 per month.
Question 5:
To find how much the amount of water in the canteen should change every 10 minutes, we divide the recommended amount of water per hour (24 ounces) by the number of minutes in an hour (60 minutes). So the quotient is 24/60, which is approximately 0.40. However, since we are looking for the change in water every 10 minutes, we multiply this quotient by the number of 10-minute intervals in an hour (6 intervals). Therefore, the amount of water in the canteen should decrease by approximately 2.40 ounces every 10 minutes.
Step 1 (Question 1): To calculate the rate of change in the squirrel's height above the ground, divide the change in height by the time it took. The change in height is 100 feet (initial height) - 45 feet (final height) = 55 feet. So, the rate of change in the squirrel's height is 55 feet / 5.25 seconds = 10.48 feet per second.
Step 1 (Question 2): To calculate the average rate of change in the dolphin's position, divide the change in altitude by the time it took. The change in altitude is 3.5 meters (highest point) - (-10 meters) (lowest depth) = 13.5 meters. So, the average rate of change in the dolphin's position is 13.5 meters / 12.5 seconds = 1.08 meters per second.
Step 1 (Question 3): To calculate the rate of change in the diver's depth, divide the change in depth by the time it took. The change in depth is -15 meters (initial depth) - (-25 meters) (final depth) = 10 meters. So, the rate of change in the diver's depth is 10 meters / 10.1 seconds = 0.99 meters per second.
Step 1 (Question 4): To find the amount the car's value decreases per month, divide the total decrease in value (which is $4,000) by the number of months (which is 12). So, the value decreases by $4,000 / 12 months = $333.33 per month.
Step 1 (Question 5): To determine the amount by which the water in the canteen should change every 10 minutes, divide the recommended amount of water per hour (which is 24 ounces) by the number of minutes in an hour (which is 60 minutes). So, the amount of water should change by 24 ounces / 60 minutes = 0.40 ounces every 10 minutes.