Chapter 5.5, Problem 1E

Use your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.

Doctors treated a patient at an emergency room from 2:00P.M. to 7:00P.M. The patient’s blood oxygen level L (in percent) during this time period can be modeled by L=0.270t2+3.59t+83.1,2t7 where t represents the time of day, with t=2 corresponding to 2:00P.M. Use the model to estimate the time (rounded to the nearest hour) when the patient’s blood oxygen level was 93 .

Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?

Find the derivative of each function.

Let f(x) be the height of a maple tree in inches and a the number of years since 2000. A linear model for the data is f(x) = 9.44x+84.182. 220 210 200 190 180 170 160 150 140 130 120 110 100 -90- 804 70 -60 -50+ 6 9 12 15 A) To the nearest inch, estimate the height of the maple tree in 2012. inches B) Use the equation to find the year in which the tree will be 246 inches tall.

Let f(x) be the height of a maple tree in inches and x the number of years since 2000. A linear model for the data is f(x) = 9.44x + 84.182. 220 210 200 190 180 170 160 150 140 130 120 110 100 -90 80 70 -60 50+ 12 A) To the nearest inch, estimate the height of the maple tree in 2011. inches B) Use the equation to find the year in which the tree will be 246 inches tall.

Use the linear approximation to estimate Af = f(3.4) – f(3) for f(x) = . (Use decimal notation. Give your answer to three decimal places.) Af = Estimate the actual change. (Use decimal notation. Give your answer to six decimal places.) Af = Compute the error and the percentage error in the linear approximation. (Use decimal notation. Give your answer to six decimal places.) The error in the Linear Approximation is (Use decimal notation Give vour answer to two decimal places) Question Source: Rogawski 4e Calculus Early Transcende

3. Consider a function involving the height over time of a ball thrown into the air. Which would be the independent variable? Which would be the dependent variable? How do you know this? Explanation:

In cold weather, we feel colder when the wind blows. This is quantified by the wind chill index W, which is supposed to predict how cold we will feel for a given air temperature T, in degrees Fahrenheit, and wind speed V, in miles/hour. The National Weather Service uses the following formula: W=35.74+0.6215T−35.75V^0.16+0.4275TV^0.16, for T≤50 and V≥3. What is the wind chill index when the air temperature is 25 degrees and the wind speed is 18 miles/hour?Answer:  Calculate the partial derivatives WT and WV when T=25 and V=18.WT= WV=  Use your answer above to do the following question: When the air temperature is 25 degrees, estimate the change in the wind chill index if the wind speed increases by 2 miles/hour from 18 miles/hour.Answer: