Question

A house appreciates (grows in value) about 6% each year. If the house is now worth 158,000, in about how many years will it be worth 200,000? Use the equation 200,000= 158,000(1.06)^x to solve this problem. Round to the nearest year

Answer 1

200,000 = 158,000(1.06)^x
Divide both sides by 158,000
1.2658 = 1.06^x
Take the log of both sides and use the power rule to bring down the exponent (x) to the front.
log 1.2658 = x log 1.06
Divide both sides by log 1.06
log (1.2658)/log(1.06) = x
x = 4 years

CHECK
y = 158,000(1.06)^4
y = 199,471.36