The linear function that models the fuel in the car's tank based on distance driven is V = -0.07x + 40, derived from the provided data points. After driving 50 km, the car would have 36.5 litres of fuel remaining in the tank.
Step-by-step explanation:
The linear equation that models the amount of fuel, V, in litres in a car's tank as a function of the distance driven, x, in kilometres is V = mx + c. Given that after driving 100 km, the fuel in the tank is 33 litres, we can form the equation 33 = m(100) + c. After driving 250 km, the amount of fuel is 22.5 litres, resulting in the equation 22.5 = m(250) + c.
To find the values of m and c, we solve this system of equations. Subtracting the first equation from the second gives a new equation -10.5 = 150m. Solving for m, we find that m = -0.07. Using this value in the first equation, we find 33 = -0.07(100) + c, which gives c = 40. Now, the complete equation is V = -0.07x + 40.
To calculate the amount of fuel in the tank after driving 50 km, we substitute x = 50 into the equation: V = -0.07(50) + 40. This results in V = 36.5 litres.