A car costs £1200 to run in its first year and subsequently the annual cost increasesby £100 each year. How much does it cost to run the second year?, third year?, fourthyear? Write down a formula for the cost £𝐶 in the 𝑥−th year
Question
A car costs £1200 to run in its first year and subsequently the annual cost increasesby £100 each year. How much does it cost to run the second year?, third year?, fourthyear? Write down a formula for the cost £𝐶 in the 𝑥−th year
Solution
The cost to run the car in the second year would be £1200 (cost of the first year) + £100 (annual increase) = £1300.
For the third year, you would add another £100 to the cost of the second year: £1300 + £100 = £1400.
For the fourth year, you would add another £100 to the cost of the third year: £1400 + £100 = £1500.
The formula for the cost £C in the x-th year would be:
C = 1200 + 100*(x-1)
This formula starts with the initial cost (£1200) and adds £100 for each year past the first year (which is why we have "x-1" in the formula).
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