A battery is being charged. The charging rate is modelled by dq/dt=k(Q-q), where q is the charge in the battery( measured in ampere hours) at time t( measured in hours), Q is the maximum charge the battery can store and k is at constant of proportionality. The model is valid for q> and equal to o.4Q.

a. It is given that q=xQ where x is a constant such that x is between 1 and 0.4- inclusive of 1 and 0.4. Solve the differential equation to find q in terms of t.

b. It is noticed that the charging rate halves every 40 minutes. Show that k=3/2 in2- notice 3/2 in2 is different from 3/2in2.

c. Charging is always stopped when q=0.95Q. If T is the time until charging is stopped, show that T=2in(20(1-x) over 3in2 for the values between 0.4 and 0.95 inclusive of these two values.

Please explain if you can as it is a word question. Explanation has equal value to working, probably more-