Need help with this math question, part E is not needed but if you can write answer then good otherwise I can manage , but need help to understand the rest of the question .

The ZENN( zero emissions no noise car )is an environmentally friendly commut car invented in Canada. The current model is powered by six rechargeable 12v batteries and has a top speed of 40km/h

The battery has the following discharge characteristics

Fully charged: 72V

Totally discharged (OV), with constant usage of 12 h.

The battery discharge is not constant, the graph shows the discharge pattern of the batteriss

During the first two hours the batterediboardeexponentially to approximately 80% of

original charge. The function for this period has the form V = a (10-lt),

where V is the

remaining voltage, r, is the time in hours, and a and k are constant.

The batterics then discharge non-linearly over the next 8 I to 70% of original charge.

The function for this period has the form V = b + Vc-t, where b and c are constants

During the last 2 h the charge drops on a steep curve to 0 V. The function for this part

is V = n(t - p)? + 9, where n, p, and q are constants.

The ZENN (Zero Emission, No Noise) car is an environmentally friendly commuter car invented ZENN and Now in Canada. The current model is power speed of 40 km/h. powered by six 12-volt rechargeable batteries and has a top The battery has the following discharge characteristics Fully charged: 72V Totally discharged (OV), with constant usage of 12 h. The battery discharge is not constant. The graph shows the discharge pattern of the batteries During the first two hours, the batteries discharge exponentially to approximately 80% of original charge. The function for this period has the form V= a (10-kt) , where V is the remaining voltage, t, is the time in hours, and a and k are constant. The batteries then discharge non-linearly over the next 8 h to 70% of original charge. The function for this period has the form V = b + Vc -t, where b and c are constants During the last 2 h the charge drops on a steep curve to 0 V. The function for this part is V = n( t - p)2 + q, where n, p, and q are constants. ZENN Car Batteries 80 _ = 32 - - 70 50 2 53.6)- 50 (10, 50.4) Voltage Stored (V) 40 30 20 10 O 36 Time (h) a) Justify in writing that the graph meets all the conditions described. b) What happened between 12 h and 24 h? c) Find the equations for the three parts of the curve, for the time interval [0, 12]. Specify any restrictions on domain and range, using appropriate mathematical notation. d) If the new rechargeable battery has a discharge time of 20 h. Describe how would affect the graph and change your answers to part c). e) Research how the cost to run this battery-powered car compares to the costs to run a compact gasoline-powered car. Write a brief report to a courier company that is planning to purchase a fleet of small cars for city deliveries