Question

The equation p = 1.65t² + 18.25t + 155 approximates the average sale price p of a house (in thousands of dollars) for years t since 2010.

What is the best estimate for the price of the house in year 2018?
$364,000
$407,000
$427,000
$453,000

Answer 1

If the equation for price is equal to 1.65t^2 + 18.25t + 155, where t is years since 2010, in order to calculate the price in 2018 we should simply substitute t = 2018-2010 = 8 into the equation. So t^2 = 64, p = 1.65*64 + 18.25*8 + 155 = 105.6 + 146 + 155 = 405.6 So the closest estimate of those given would be $407,000.

Answer 2

Given that the price has been estimated using the model:
p=1.65t^2+18.25t+155
setting 2010 to represent zero, then from 2010-2018=8 years
thus
p(8)=1.65*8^2+18.25*8+155
=406.6
thus our total estimated price will be:
$406600 this is approximately equal to $407000
hence the answer is B