Question

10. The value of a new car decreases by 15% each year. The value (D) of the car after t years could be modelled as D = 23000(1 - 0.15) a) Show that the cost of the new car was £23 000. b) What is the cost of the car after 6 years? c) If we drew a graph, what would be the equation of the asymptote? - I just need help with question c ​

Answer 1

y = 0

Explanation:

The function has a horizontal asymptote at y = 0 where y is the value of the car

`\text{Since the equation for the value of the car is }`
`23000(1-0.15)^t`

As
`t \rightarrow \infty, \text{the term } (1-0.15)^t \rightarrow 0 \\`

This is because the term (1-0.15) is < 1 and a nˣ approaches 0 as x → ∞ since the values get smaller and smaller with increasing powers of x

So the equation for the horizontal asymptote is y = 0

Provided graph to illustrate