1. Which of the following statements represent EXPONENTIAL relationships? Check all that apply.
a. The temperature is decreasing at the rate of 3°F per hour.
b. The value of a car depreciates at a rate of 22% per year.
c. The price of houses in this neighborhood is increasing at the rate of about 3% per year.
d. The population of your home town is doubling every 12 years.
Te. he number of cars in the parking lot is decreasing at the rate of 5 cars per hour.
b , c , d
Te. he number of cars in the parking lot is decreasing at the rate of 5 cars per hour.
The statements that represent exponential relationships are:
b. The value of a car depreciates at a rate of 22% per year.
d. The population of your home town is doubling every 12 years.
To determine which of the statements represent exponential relationships, let's analyze each statement:
a. The temperature is decreasing at the rate of 3°F per hour.
This statement does not represent an exponential relationship since the temperature decrease is constant and linear, not exponential.
b. The value of a car depreciates at a rate of 22% per year.
This statement represents an exponential relationship. The car's value decreases by a constant percentage each year, leading to exponential depreciation.
c. The price of houses in this neighborhood is increasing at the rate of about 3% per year.
This statement does not represent an exponential relationship since the price increase is constant and linear, not exponential.
d. The population of your hometown is doubling every 12 years.
This statement represents an exponential relationship. The population is growing exponentially because it is doubling every fixed period of time (12 years).
e. The number of cars in the parking lot is decreasing at the rate of 5 cars per hour.
This statement does not represent an exponential relationship since the car count decrease is constant and linear, not exponential.
Therefore, the statements representing exponential relationships are:
b. The value of a car depreciates at a rate of 22% per year.
d. The population of your hometown is doubling every 12 years.