Donald fills his gasoline tank before leaving on a trip. His car uses gasoline at a constant rate and the amount of gasoline, g, remaining after m miles can be

Question

modeled by m + 20g = 640.
Select the correct values to complete the range of the function in context.

Answer 1

To analyze the situation described in the equation \( m + 20g = 640 \), we can rewrite this to express \( g \) in terms of \( m \):

\[ 20g = 640 - m \] \[ g = \frac{640 - m}{20} \]

This function indicates that the remaining amount of gasoline \( g \) is dependent on the number of miles \( m \) traveled.

1. Find the Constraints:
   • Since \( g \) represents the gallons of gasoline remaining, it cannot be negative. Therefore, we need \( g \geq 0 \).
   • Setting \( g = 0 \) in our equation gives us:

\[ 0 = \frac{640 - m}{20} \]

Multiplying both sides by 20 results in:

\[ 640 - m = 0 \implies m = 640 \]

So the maximum distance \( m \) that can be traveled with a full tank without running out of gas is 640 miles.

2. Minimum Value of \( m \):

   • The minimum distance that can be traveled is \( m = 0 \).

3. Determine the Values of \( g \):

   • At \( m = 0 \): \[ g = \frac{640 - 0}{20} = \frac{640}{20} = 32 \]
   • At \( m = 640 \): \[ g = \frac{640 - 640}{20} = 0 \]

4. Range of Function:

   • Therefore, as \( m \) varies from 0 to 640, \( g \) will vary from 32 gallons (when \( m = 0 \)) to 0 gallons (when \( m = 640 \)).
   • Thus, the range of the function in this context is:

\[ g \in [0, 32] \]

In conclusion, the completed range of values for gasoline remaining \( g \) as a function of miles traveled \( m \) in this context is \( g \in [0, 32] \).