Question

A $2,000 bicycle depreciates at a rate of 10% per year.After how many years will it be worth less than $1,000?o 5 yearso 7 yearso 10 yearso 100 years

Answer 1

A $2,000 bicycle depreciates at a rate of 10% per year.

After how many years will it be worth less than $1,000?

o 5 years

o 7 years

o 10 years

o 100 years

we know that

the equation that represent this problem is equal to

`y=a(1-r)^x`

where

y -----> the value of the bici

a=2,000

r=0.10

substitute

For y=1,000

`\begin{gathered} 1,000=2,000(1-0,10)^x \\ 0.5=0.9^x \\ \log (0.5)=x\cdot\log (0.90) \\ x=6.57\text{ years} \end{gathered}`

greater than 6.57 years

answer is 7 years