The table of values below represents a linear function and shows Marco's progress as he is pumping gas into his car. What is the output for the initial value?
| Gallons of Gas | 0 | 12 | 24 | 36 | 48 |
|---|---|---|---|---|---|
| Cost of Gallons in Car | 3 | 5 | 7 | 9 | 11 |
A. 0 gallons
B. 2 gallons
C. 3 gallons
D. 6 gallons
Answer (1)
The problem provides a table representing a linear function of gas pumped into a car.
The initial value is the output when the input is 0.
From the table, when the input (time) is 0, the output (gallons of gas) is 3.
Therefore, the output for the initial value is 3 gallons.
Explanation
Understanding the Problem We are given a table of values representing a linear function that shows Marco's progress as he is pumping gas into his car. We need to find the output (gallons of gas) for the initial value (time = 0).
Identifying the Initial Value The initial value corresponds to the y-intercept of the linear function, which is the value of the function when the input (x) is 0.
Reading the Table From the table, we can see that when the time (Merries Spert Purpres Gess) is 0, the amount of gas in the car (Calces of Genin Car) is 3 gallons.
Final Answer Therefore, the output for the initial value is 3 gallons.
Examples
Understanding initial values is crucial in many real-life scenarios. For instance, when you start a savings account with an initial deposit, that deposit is the initial value. As you add more money over time, the account balance grows linearly (assuming no interest). Similarly, when you fill a tank with water, the initial amount of water is the initial value, and the rate at which you add water determines the linear increase in the water level. Recognizing and interpreting initial values helps in making informed decisions and predictions in various practical situations.
