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Concept explainers
Median Home Prices The median home price in the United States over the period January 2010–January 2015 can be approximated by
P(t)=0.4.5t2−15t+180 thousand dollars (0≤t≤5), where t is time in years since the start of 2010.66
a. Compute the average rate of change of P(t) over the interval [1,5], and interpret your answer. [HINT: See Example 3 of section 10.4.]
b. Estimate the instantaneous rate of change of P(t)
at t=1 andinterpret your answer. [HINT: See Example 2 (a).]
c. The answer to part (a) and part (b) have opposite signs. What does this indicate about the price?
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- Instructions. "I have written solutions in text form, but I need experts to rewrite them in handwriting from A to Z, exactly as I have written, without any changes."arrow_forwardBoth in images okk. Instructions. "I have written solutions in text form, but I need experts to rewrite them in handwriting from A to Z, exactly as I have written, without any changes."arrow_forwardQuestion 1: If a barometer were built using oil (p = 0.92 g/cm³) instead of mercury (p = 13.6 g/cm³), would the column of oil be higher than, lower than, or the same as the column of mercury at 1.00 atm? If the level is different, by what factor? Explain. (5 pts) Solution: A barometer works based on the principle that the pressure exerted by the liquid column balances atmospheric pressure. The pressure is given by: P = pgh Since the atmospheric pressure remains constant (P = 1.00 atm), the height of the liquid column is inversely proportional to its density: Step 1: Given Data PHg hol=hgx Poil • Density of mercury: PHg = 13.6 g/cm³ Density of oil: Poil = 0.92 g/cm³ • Standard height of mercury at 1.00 atm: hμg Step 2: Compute Height of Oil = 760 mm = 0.760 m 13.6 hoil = 0.760 x 0.92 hoil = 0.760 × 14.78 hoil = 11.23 m Step 3: Compare Heights Since oil is less dense than mercury, the column of oil must be much taller than that of mercury. The factor by which it is taller is: Final…arrow_forward
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