You bought your first car for £2300. Your insurance will probably cost you more! Honestly it will.
You will pay more for your insurance than you will the car, but you will love your first car.
To make matters worse it lost 25% of its value in the first year and 18% of its value in the second year.
What is the value of your car at the end of the second year? Can you even bear to think about it?
This is a great example of repeated proportional change which can be used to predict changes over a period of time.
All you are going to do is apply a percentage increase or decrease or (maybe even both) more than once.
You could decrease by 25% and then again by 18% but that could be time consuming.
Mathematicians are always looking for something a little quicker.. a bit like your car.
A quick recap
To find a percentage increase or decrease you use a multiplier.
Increase 65 by 23% 65 x 1.23 = 79.95
Decrease 80 by 42% 80 x 0.58 = 46.40 (100% - 42% = 58% which gives our multiplier)
With growth and decay problems you need to apply these formulas more than once.
Top tip - use your multipliers at the same time.
Now back to trying to calculate the value of your car.
100 - 25 = 75 (0.75) For the first decrease
100 - 18 = 82 (0.82) For the second decrease
0.75 x 0.82 = 0.615
£2300 x 0.615 = £1414.50
It is enough to make you cry like a baby isn't it.. all that money lost.
Like wise to increase anything e.g 320 by 2% and the 3.5%
2 x 3.5 = 7 (Multiplier is 1.07)
320 x 1.07 =342.40
Top tip - don't be tempted to round your multipliers it could throw out your final answers