Question

1. the median home price in a country over the period january 2011 to january 2017 can be approximated by ( p(t) = 3.7t^2 - 11t + 150 ) thousand dollars, where ( t ) is time in years since the start of 2011. what was the average rate of change of the median home price from the start of 2013 to the start of 2015?

Explanation:

Step1: Determine t values

For start of 2013, \( t = 2013 - 2011 = 2 \). For start of 2015, \( t = 2015 - 2011 = 4 \).

Step2: Calculate P(2)

Substitute \( t = 2 \) into \( P(t) = 3.7t^2 - 11t + 150 \):
\( P(2) = 3.7(2)^2 - 11(2) + 150 = 3.7(4) - 22 + 150 = 14.8 - 22 + 150 = 142.8 \)

Step3: Calculate P(4)

Substitute \( t = 4 \) into \( P(t) \):
\( P(4) = 3.7(4)^2 - 11(4) + 150 = 3.7(16) - 44 + 150 = 59.2 - 44 + 150 = 165.2 \)

Step4: Find average rate of change

Average rate of change formula: \( \frac{P(4) - P(2)}{4 - 2} \)
Substitute values: \( \frac{165.2 - 142.8}{2} = \frac{22.4}{2} = 11.2 \)

Answer:

The average rate of change is 11.2 thousand dollars per year.