Problema Solution
If a painting costs $45 and its value increases at the rate of 8% each year, how many years will it take for its value to double?
Answer provided by our tutors
Beginning (after 0 years) the painting costs: $45
After 1 year the cost increases by 8%: 45 + 0.08*45 = 45(1 + 0.08) = 45*1.08
After 2 year the cost increases by 8% compared to the previous year: 45*1.08 + 0.08*45*1.08 = 45*1.08(1 + 0.08) = 45*1.08^2
........
After t years the cost of the painting will be: 45*1.08^t
We need to find t such that the value is equal to 2*45 = 90 (double):
45*1.08^t = 2*45
........
click here to see the equation solved for t
........
t = 9 years approximately
After 9 years the value of the painting will double.