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# C4 Differential Equations help! watch

1. The question:
The new price of a particular make of car is £10000
When it is t years, the list price is £V. When t = 5, V = 5000

The rate of depreciation is constant. Write this as a differential equation.
Solve the differential equation and hence find the value of a car that is 7 years old according to this model.

Explain why this model breaks down for large values of t.

My response:
• When t = 0 V = 10000
• V = kt
• 5000 = 5k
• k = 1000?

-dv/dt = kt
-dv/dt = 1000 x 7
dv/dt =-7000

So therefore the value has decreased by £7,000 in 7 years, meaning the model would break down if t > 10 because the depreciation would be more than the original price of the car?

I don't feel that I have answered this question correctly as I struggle to change the wording into the equation, any help would be greatly appreciated!
2. (Original post by Elucia)
I don't feel that I have answered this question correctly as I struggle to change the wording into the equation, any help would be greatly appreciated!
You were told that the rate of depreciation was constant

So

You need to solve this by doing

Then use the 2 pieces of information that you have to find c and k

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