Median Home Prices The median home price in a certain country over the period January 2010–January 2015 can be approximated by P(t) = 3.5t2 − 14t + 120 thousand dollars (0 ≤ t ≤ 5), where t is time in years since the start of 2010. (a) Compute the average rate of change of P(t) over the interval [1, 5]. $ thousand per year Interpret your answer. In this country, the median home price was growing at an average rate of about $ thousand per year over the 4-year period beginning at the start of 2011. (b) Estimate the instantaneous rate of change of P(t) at t = 1. (Round your answer to three decimal places.) $ thousand per year Interpret your answer. In this country, the median home price was dropping at an instantaneous rate of about $ thousand per year at the start of 2011. (c) The answers to parts (a) and (b) have opposite sign. What does this indicate about the median home price in this country? The median home price was decreasing at the start of 2011 but over the subsequent three years bottomed out and began to increase significantly, making the average rate of change negative.The median home price was increasing at the start of 2011 but over the subsequent three years topped out and began to decrease significantly, making the average rate of change positive. The median home price was decreasing at the start of 2011 but over the subsequent three years bottomed out and began to increase significantly, making the average rate of change positive.The median home price was increasing at the start of 2011 but over the subsequent three years topped out and began to decrease significantly, making the average rate of change negative.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

Median Home Prices The median home price in a certain country over the period January 2010–January 2015 can be approximated by

P(t) = 3.5t² − 14t + 120 thousand dollars (0 ≤ t ≤ 5),

where t is time in years since the start of 2010.

(a)

Compute the average rate of change of P(t) over the interval [1, 5].

$ thousand per year

Interpret your answer.

In this country, the median home price was growing at an average rate of about $ thousand per year over the 4-year period beginning at the start of 2011.

(b)

Estimate the instantaneous rate of change of P(t) at t = 1. (Round your answer to three decimal places.)

$ thousand per year

Interpret your answer.

In this country, the median home price was dropping at an instantaneous rate of about $ thousand per year at the start of 2011.

(c)

The answers to parts (a) and (b) have opposite sign. What does this indicate about the median home price in this country?

The median home price was decreasing at the start of 2011 but over the subsequent three years bottomed out and began to increase significantly, making the average rate of change negative.The median home price was increasing at the start of 2011 but over the subsequent three years topped out and began to decrease significantly, making the average rate of change positive. The median home price was decreasing at the start of 2011 but over the subsequent three years bottomed out and began to increase significantly, making the average rate of change positive.The median home price was increasing at the start of 2011 but over the subsequent three years topped out and began to decrease significantly, making the average rate of change negative.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

Expert Solution