For time $t \geq 0$ hours, let $r ( t ) = 120 \left( 1 - e ^ { - 10 t ^ { 2 } } \right)$ represent the speed, in kilometers per hour, at which a car travels along a straight road. The number of liters of gasoline used by the car to travel $x$ kilometers is modeled by $g ( x ) = 0.05 x \left( 1 - e ^ { - x / 2 } \right)$. (a) How many kilometers does the car travel during the first 2 hours? (b) Find the rate of change with respect to time of the number of liters of gasoline used by the car when $t = 2$ hours. Indicate units of measure. (c) How many liters of gasoline have been used by the car when it reaches a speed of 80 kilometers per hour?
For time $t \geq 0$ hours, let $r ( t ) = 120 \left( 1 - e ^ { - 10 t ^ { 2 } } \right)$ represent the speed, in kilometers per hour, at which a car travels along a straight road. The number of liters of gasoline used by the car to travel $x$ kilometers is modeled by $g ( x ) = 0.05 x \left( 1 - e ^ { - x / 2 } \right)$.
(a) How many kilometers does the car travel during the first 2 hours?
(b) Find the rate of change with respect to time of the number of liters of gasoline used by the car when $t = 2$ hours. Indicate units of measure.
(c) How many liters of gasoline have been used by the car when it reaches a speed of 80 kilometers per hour?