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Liono4ka [1.6K]
2 years ago
9

You purchased a rare painting for $150 that is increasing in value by 3% annually. How many years will it take until it is doubl

ed in value? Round to the nearest whole year
Mathematics
1 answer:
Ahat [919]2 years ago
6 0

Answer:

23 years.

Step-by-step 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=\dfrac{\log 2}{\log (1.03)}

t=23.44977

t\approx 23

Therefore, the required number of years is 23.

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