ECON 220 (6)

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Homework 6

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Section 10.4 (6 points)

1. The table below shows U.S. daily imports from Mexico, for 2001-2009 (t=1 represents

the start of 2001):

t

(year since 2000) 1 2 3 4 5 6 7 8 9

I(t)

(million barrels) 1.4 1.35 1.5 1.55 1.6 1.5 1.5 1.5 1.2

a. Use the data in the table above to compute the average rate of change I(t) over the

period 2001-2006. Interpret the result (3 points)

2. The median home price in the U.S. over the perio2003-2011 can be approximated by

𝑃(𝑡) = −5𝑡2 + 75𝑡 − 30 thousand dollars (3 ≤ t ≤ 11),

Where t is the time in years since the start of 2000.

a. What was the average rate of change of the median home price from the start of

2007 to the start of 2009? (3 points)

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Section 10.5 (16 points) In the questions below, use the balanced difference quotient method to estimate the

derivative of the given function at the indicated point. (Hint, use h = 0.0001)

(3 points each)

3. 𝑠(𝑡) = 1

𝑡3 ; estimate 𝑠′(−2)

4. 𝑦 = 1 − 𝑥2; estimate ⅆ𝑦

ⅆ𝑥 |

𝑥=−1

5. Use any method to

(a)estimate the slope of the tangent to the graph of the function 𝑓(𝑥) = 2𝑥 + 4 ; 𝑥 = −1

at the point with the given x-coordinate (𝑥 = −1) (3 points)

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(b) find an equation of the tangent line in part (a). (3 points)

6. Suppose the demand for a new brand of sneakers is given by

𝑞 = 5,000,000

𝑝

Where 𝑝 is the price per pair of sneakers, in dollars, and q, is the number of pairs of

sneakers that can be sold at price 𝑝

a. Find 𝑞(100) (1 point)

b. Estimate 𝑞′(100) Using ordinary difference quotient and the h = 0.0001 (3 points)