Median Home Prices The median home price in a certain country over the period January 2010-January 2015 can be approximated by P(t) = 4.5t2 - 17t + 120 thousand dollars (0 sts 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? O 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. O 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. O 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. O 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.
Median Home Prices The median home price in a certain country over the period January 2010-January 2015 can be approximated by P(t) = 4.5t2 - 17t + 120 thousand dollars (0 sts 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? O 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. O 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. O 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. O 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.
Calculus For The Life Sciences
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ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.1: Techniques For Finding Derivatives
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![Median Home Prices The median home price in a certain country over the period January 2010-January 2015 can be approximated by
P(t) = 4.5t2 – 17t + 120 thousand dollars (0 sts 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?
O 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.
O 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 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.
O 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3846dbf-69f8-45b6-999f-7956e81b865c%2Fd23fdd1d-ec82-42cd-90c5-b021be750f73%2Fh68fyur_processed.png&w=3840&q=75)
Transcribed Image Text:Median Home Prices The median home price in a certain country over the period January 2010-January 2015 can be approximated by
P(t) = 4.5t2 – 17t + 120 thousand dollars (0 sts 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?
O 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.
O 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 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.
O 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.
Expert Solution
Step 1
Given:-
Median Home Prices The median home price in a certain country over the period January 2010-January 2015 can be approximated by
P(t) = 4.5t² -17t + 120 thousand dollars (0 ≤ t ≤ 5),
where t is time in years since the start of 2010.
To find:-
(a) Compute the average rate of change of P(t) over the interval [1, 5].
(b) Estimate the instantaneous rate of change of P(t) at t = 1.
(c) The answers to parts (a) and (b) have opposite sign. What does this indicate about the median home price in this country?
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