You buy a painting for $1500. The art work increases by 50% annually. When will the painting have a value of $10,000?
1500 + 1500*0.5*t = 10000,
t = ?.
To find out when the painting will have a value of $10,000, we can use a simple mathematical formula.
Let's assume that the number of years it takes for the painting to reach a value of $10,000 is represented by 'n'.
We know that the painting increases in value by 50% every year. So, the value of the painting after the first year would be:
$1500 + (50% of $1500) = $1500 + ($1500 * 0.50) = $1500 + $750 = $2250
Similarly, the value after the second year would be:
$2250 + (50% of $2250) = $2250 + ($2250 * 0.50) = $2250 + $1125 = $3375
Following the same logic, we can generalize the formula for finding the value of the painting after 'n' years:
Value after 'n' years = $1500 * (1 + 0.50)^n
Now, we can set up an equation to find the value of 'n' when the painting reaches $10,000:
$1500 * (1 + 0.50)^n = $10,000
Dividing both sides of the equation by $1500, we get:
(1 + 0.50)^n = $10,000 / $1500 = 6.67
To solve for 'n', we need to take the logarithm of both sides of the equation. By using the logarithmic property, we can solve for 'n':
n * log(1 + 0.50) = log(6.67)
Finally, we can solve for 'n' by dividing both sides of the equation by log(1 + 0.50):
n = log(6.67) / log(1 + 0.50)
Using a calculator, we can evaluate the right side of the equation, which gives us:
n ≈ 4.34
Since 'n' represents the number of years, it is not possible to have a fraction of a year. Therefore, rounding up the value of 'n' to the nearest whole number, we find that the painting will have a value of $10,000 after approximately 5 years.