Question

B) The price of a house increases exponentially over time. A house presently costs $400,000, and it future

value can be modeled by the equation: A = 400,000 (1.04)*, where A is the value of the home after x years.
i) What percent is the house's value going up each year?
ii) What is the value of the home in 15 years?
ii) Assuming the trend continues, when will the value of the home double?
+4

Answer 1

Answer: The percent that the house's value is going up each year is given by the factor 1.04 - 1, which is 0.04. This represents a 4% increase in the value of the house each year.

ii) To find the value of the home in 15 years, you can substitute x = 15 into the equation to get:

A = 400,000 (1.04)^15

= 400,000 (1.7589)

= 700,356

Therefore, the value of the home in 15 years is $700,356.

iii) To find when the value of the home will double, you can set the value of A equal to 2*400,000 and solve for x:

2*400,000 = 400,000 (1.04)^x

2 = (1.04)^x

x = log(2)/log(1.04)

= 10.67

Therefore, it will take approximately 10.67 years for the value of the home to double, assuming the trend continues.