6. The number of people, x, in a queue at a travel centre t minutes after it opens is modelled by a differential equation dx/dt= 1.4t-0.5x for values of t up to 10. Sovlve the differential equation given that x=8 when t=o.

b. An alternative model gives the differential equation dx/dt= 1.4t-o.5x for the same values of t. Verify that x=13.6e^-0.5t+2.8t-5.6 satisfies this differential equation. Verify also that when t=0 this function takes the value 8.

Please give working and explantion