Questions: Which of the following statements represent EXPONENTIAL functions? Check all that apply. The price of houses in this neighborhood is increasing at the rate of about 3% per year. The value of a car depreciates at a rate of 22% per year. The population of your home town is doubling every 12 years.

Which of the following statements represent EXPONENTIAL functions? Check all that apply.
The price of houses in this neighborhood is increasing at the rate of about 3% per year.
The value of a car depreciates at a rate of 22% per year.
The population of your home town is doubling every 12 years.

Transcript text: Which of the following statements represent EXPONENTIAL functions? Check all that apply. The number of cars in the parking lot is decreasing at the rate of 5 cars per hour. The price of houses in this neighborhood is increasing at the rate of about $3 \%$ per year. The value of a car depreciates at a rate of $22 \%$ per year. The population of your home town is doubling every 12 years. The temperature is decreasing at the rate of $3^{\circ} \mathrm{F}$ per hour.

Solution

Solution Steps

To determine which statements represent exponential functions, we need to identify scenarios where a quantity changes by a constant percentage over equal time intervals. This is characteristic of exponential growth or decay.

A constant decrease of 5 cars per hour is linear, not exponential.
An increase of 3% per year is exponential because it involves a constant percentage change.
A depreciation of 22% per year is exponential for the same reason.
Doubling every 12 years is exponential as it involves a consistent multiplicative change.
A decrease of 3°F per hour is linear, not exponential.

Step 1: Identify Exponential Functions

To determine which statements represent exponential functions, we look for scenarios where a quantity changes by a constant percentage over equal time intervals. This is characteristic of exponential growth or decay.

Step 2: Analyze Each Statement

Statement 1: "The number of cars in the parking lot is decreasing at the rate of 5 cars per hour."
This represents a linear decrease, not exponential.
Statement 2: "The price of houses in this neighborhood is increasing at the rate of about $3\%$ per year."
This indicates exponential growth since it involves a constant percentage increase.
Statement 3: "The value of a car depreciates at a rate of $22\%$ per year."
This also represents exponential decay due to the constant percentage decrease.
Statement 4: "The population of your home town is doubling every 12 years."
This is a classic example of exponential growth, as the population increases by a factor of 2 over a fixed time period.
Statement 5: "The temperature is decreasing at the rate of $3^{\circ} \mathrm{F}$ per hour."
This is another linear change, not exponential.

Step 3: Compile Exponential Statements

From the analysis, the statements that represent exponential functions are:

The price of houses in this neighborhood is increasing at the rate of about $3\%$ per year.
The value of a car depreciates at a rate of $22\%$ per year.
The population of your home town is doubling every 12 years.

Final Answer

The statements that represent exponential functions are:

The price of houses in this neighborhood is increasing at the rate of about $3\%$ per year.
The value of a car depreciates at a rate of $22\%$ per year.
The population of your home town is doubling every 12 years.

Thus, the answer is: \[ \boxed{\text{Statements 2, 3, and 4 are exponential functions.}} \]

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