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Math Asked by a SnapAndSolve user · about 2 hours ago

Mary is selling candles. On Monday she sold 5 candles for $8 and on Wednesday she sold 7 candles for $11....

1. Mary is selling candles. On Monday she sold 5 candles for $8 and on Wednesday she sold 7 candles for $11. What is the rate of change?
2. After 2 minutes of swimming a scuba diver was 7 feet below sea level. After 3 minutes the scuba diver was 10 feet below sea level. What is the rate of change?
3. You are keeping track of the temperature change outside and notice that at 2 hours the temperature was 25 degrees, and at 6 hours the temperature was 15 degrees. What is the rate of change?
4. The snowbank outside your house is melting. At one hour, the height of the snowbank is 48 inches tall, and at 5 hours the height of the snowbank is 45 inches tall. What is the rate of change?

Answer

  1. The rate of change is calculated as the change in cost divided by the change in the number of candles. From Monday to Wednesday, the change in cost is $11 - $8 = $3, and the change in the number of candles is 7 - 5 = 2. Therefore, the rate of change is $3/2 candles = $1.50 per candle.

  2. The rate of change is calculated as the change in depth divided by the change in time. From 2 minutes to 3 minutes, the change in depth is 10 feet - 7 feet = 3 feet, and the change in time is 3 minutes - 2 minutes = 1 minute. Therefore, the rate of change is 3 feet per minute.

  3. The rate of change is calculated as the change in temperature divided by the change in time. From 2 hours to 6 hours, the change in temperature is 15 degrees - 25 degrees = -10 degrees, and the change in time is 6 hours - 2 hours = 4 hours. Therefore, the rate of change is -10 degrees/4 hours = -2.5 degrees per hour.

  4. The rate of change is calculated as the change in height divided by the change in time. From 1 hour to 5 hours, the change in height is 45 inches - 48 inches = -3 inches, and the change in time is 5 hours - 1 hour = 4 hours. Therefore, the rate of change is -3 inches/4 hours = -0.75 inches per hour.

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