Consider the amount of gas in your car during a road trip. You start out with 45 gallons and drive for 4 hours, leaving you with 27 gallons in the tank. You stop for lunch for 2 hours and then drive for 2 more hours, leaving you with 18 gallons.
t= time
C (t)=_____ if 0 </ t </ 4
C (t)=_____ if 4 < t </ 6
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10
To determine the amount of gas in your car at different times during the road trip, we can analyze the given information.
Let's define the amount of gas in your car, represented by the variable C(t), where t represents the time elapsed during the road trip.
Given that you start with 45 gallons of gas and drive for 4 hours, we can calculate the rate at which gas is being consumed. We divide the difference in gas (45 - 27 = 18 gallons) by the time spent driving (4 hours) to find the rate of consumption:
Rate of consumption = (45 - 27) / 4 = 18 / 4 = 4.5 gallons per hour.
Therefore, the equation for C(t) during the driving portion of the road trip (0 ≤ t ≤ 4) is:
C(t) = 45 - (4.5 * t)
Next, we know that you stop for lunch for 2 hours, during which no gas is consumed. So after the 2-hour lunch break, the amount of gas in your car remains the same, which is 27 gallons.
After the lunch break (4 < t ≤ 6), the equation for C(t) will be constant:
C(t) = 27
To summarize:
C(t) = 45 - (4.5 * t) if 0 ≤ t ≤ 4
C(t) = 27 if 4 < t ≤ 6