How to solve rates of change questions?

If the question is about something losing value, for example a cars value depreciates at a rate of 30% a year after 4 years how much will the car be worth? You are also given that at year 0 it was worth £10,000. Therefore in order to solve it you can either solve it year by year with the percentage change converted into a decimal of 0.7. This is because 1 would represent no percentage change so 100%. A 30% depreciation would therefore only represent 70% of the original value and converting 70% to a decimal gives you 0.7. So for example: Year 1= 10,000 x 0.7 = 7000 Year 2 = 7000 x 0.7 = 4900 Year 3 = 4900 x 0.7 = 3430 Year 4 = 3430 x 0.7 = 2401 An alternative method (and a quicker one) would be to calculate the value of the car after 4 years straight away. For this you take the original value (£10,000) and times it by 0.7^4. You times 0.7 by the power of 4 as this is the 4 years that the car is losing value. 10,000 x 0.7^4 = 2401 Both these methods give the same answer.