Question

You purchased a rare painting for $150 that is increasing in value by 3% annually. How many years will it take until it is doubled in value? Round to the nearest whole year

Answer 1

23 years.

Explanation:

It is given that the initial price of painting is $150 and its values increasing by 3% annually.

We need to find how many years will it take until it is doubled in value.

The value of painting after t years is given by

`y=150(1+0.03)^t`

`y=150(1.03)^t`

The value of painting after double is 300. Substitute y=300.

`300=150(1.03)^t`

Divide both sides by 150.

`2=(1.03)^t`

Taking log both sides.

`\log 2=\log (1.03)^t`

`\log 2=t\log (1.03)`

`t=(\log 2)/(\log (1.03))`

`t=23.44977`

`t\approx 23`

Therefore, the required number of years is 23.