The price of a new car on 1 January 2021 is $120 888.00. Given that the value of the car depreciates in such a way that, $n$ months after the purchase, the sale price, $P, is determined by the formula
$P = 120888e^{-0.015n},$
estimate

(i)
the sale price of the car after 1 year, giving your answer correct to the nearest $1000,
(ii)
the month and year when the sale price of the car is less than $50 000.

It won't just hand you the answer — it asks where you're stuck.How the checker works

Worked solution

1. Convert the time period to months and substitute into the given formula

1 year = 12 months.
Substitute $n = 12$ into $P = 120888e^{-0.015n}$ :
$P = 120888e^{-0.015(12)}$
$P = 120888e^{-0.18}$

2. Calculate the value and round to the nearest $1000

$P \approx 100974.15$
Rounding to the nearest $1000, we get $101 000.

Answer

$101 000

AI analysis — may contain mistakes.

Worked this one out on paper? Snap your steps and Gigle's AI math checker will circle the step where it went wrong.