A certain house costs $285,00. It is estimated that the price of the house will

Question

A certain house costs $285,00. It is estimated that the price of the house will rise 5% each year. If the prices actually rise at that rate, what will the price, P, of the house equal in y years? Fill in the table below for the price of the house in each year after the start (year o): Explain how you calculated the price of the house for each year. What number do you need to use if you want to multiply the output value for year 3 to get the value for year 4? Use your multiplier in part (e) as the base and write the rule for an exponential function for P, the price in y years. Use your equation to calculate the value of the house in 25 years.

Explanation / Answer

a) P(0 years) = $285,000

P(1 year) = $285,000 * (1 + 5/100) = $299,250

P(2 year) = 285000 * (1.05)^2 = $314212.5

P(3 year) = 285000 * (1.05)^3 = $329923.125

P(4 year) = 285000 * (1.05)^4 = $346419.28125

b) Since it is an increasing in 5% which is constant, hence we can get the price by multiplying the initial year price by 1.05

c) The number will be equal to 1.05

d) P(y years) = $285000 * (1.05)^y

e) P(25) = $285000 * (1.05)^(25) = $965,111.16

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