Question

A $1045 washing machine in a laundrymat is depreciated for tax purposes at a rate of $95 per year. Find a function for the depreciated value of the washing machine as it varies with time. When does the depreciated value reach $0?

Answer 1

let's go through the years

1045 - 95 <--- 1 year 1045 - 95(1)
1045 - 95 - 95 <--- 2 year 1045 - 95(2)
1045 - 95 - 95 - 95 <--- 3rd year 1045 - 95(3)
1045 - 95 - 95 - 95 - 95 <---- 4th year 1045 - 95(4)
1045 - 95 - 95 - 95 - 95 - 95 <--- 5th year 1045 - 95(5)
thus
1045 - 95(t) <--- after "t" years, where t > 0

so the price P = 1045 - 95t

when does it reach 0? when P = 0


`\bf 0=1045-95t\implies 95t=1045\implies t=\cfrac{1045}{95}\implies \boxed{t=11}`

Answer 2

V = value

t = time ( number of years)

so V=1045 - 95t

to find the number of years to reach 0

0=1045-95t

1045=95t

t=11 years