Question

read the situations and decide if each is best modeled by exponential growth, exponential decay, or neither. drag and drop \exponential growth\, \exponential decay\, or
either\ into the boxes to correctly classify each situation. situation | exponential growth, exponential decay, or neither a pool is drained at a constant rate of 30 gallons per hour. | dashed box the value of a motorcycle loses 13% of its value each year. | dashed box the number of students sick with the flu doubles each week. | dashed box a job mowing lawns earns you $17 per lawn. | dashed box a bank account earns interest each month at a rate of 0.07%. | dashed box

Explanation:

Step1: Analyze the first situation

A pool is drained at a constant rate of 30 gallons per hour. This is a linear decrease (constant rate), so it's neither exponential growth nor decay.

Step2: Analyze the second situation

The value of a motorcycle loses 13% of its value each year. Losing a percentage of value each year means the value is multiplied by a constant factor (1 - 0.13 = 0.87) each year, which is exponential decay.

Step3: Analyze the third situation

The number of students sick with the flu doubles each week. Doubling each week means the number is multiplied by 2 each week, which is exponential growth.

Step4: Analyze the fourth situation

A job mowing lawns earns you $17 per lawn. This is a constant amount per lawn, linear (proportional to number of lawns), so neither.

Step5: Analyze the fifth situation

A bank account earns interest each month at a rate of 0.07%. Earning interest (a percentage of the current amount) means the amount is multiplied by a constant factor (1 + 0.0007) each month, which is exponential growth.

Answer:

• A pool is drained at a constant rate of 30 gallons per hour: Neither
• The value of a motorcycle loses 13% of its value each year: Exponential Decay
• The number of students sick with the flu doubles each week: Exponential Growth
• A job mowing lawns earns you $17 per lawn: Neither
• A bank account earns interest each month at a rate of 0.07%: Exponential Growth