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MATH 152 MATH 152 Applied Calculus Applied Calculus Slides may change Slides may change

MATH 152 Applied Calculus Slides may change. Estimate 5.2

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Page 1: MATH 152 Applied Calculus Slides may change. Estimate 5.2

MATH 152MATH 152Applied CalculusApplied Calculus

Slides may changeSlides may change

Page 2: MATH 152 Applied Calculus Slides may change. Estimate 5.2

Estimate 6

0)( dxxf

5.2

Page 3: MATH 152 Applied Calculus Slides may change. Estimate 5.2

New Plants

Which species has the most plants after one year? Two years?

5.4

Page 4: MATH 152 Applied Calculus Slides may change. Estimate 5.2

A Drive Starts 100 miles north from home. When is he farthest from home? How far away? When is he closest to home? How far away?

5.4

Page 5: MATH 152 Applied Calculus Slides may change. Estimate 5.2

Bioavailability − AUCBioavailability − AUC

Cp (IV dose)

Cp (oral dose)

Cp = plasma concentration

• Find absolute bioavailability F.• It is the ratio of the areas under the plasma concentration vs time curve (AUC), assuming equal doses.

http://www.chm.davidson.edu/erstevens/AUC/AUC.html

5.4

Page 6: MATH 152 Applied Calculus Slides may change. Estimate 5.2

Theater Tickets Figure 7.4.1 is a graph of the rate r (in

arrivals per hour) at which patrons arrive at the theater in order to get rush seats for the evening performance.

The first people arrive at 8 a.m. The ticket windows open at 9 a.m. Suppose that once the windows open

people can be served at an (average) rate of 200 per hour.

7.3

Page 7: MATH 152 Applied Calculus Slides may change. Estimate 5.2

r Theater Arrivals Per Hour7.3

Page 8: MATH 152 Applied Calculus Slides may change. Estimate 5.2

Questions Find the following: The length of the line at 9 am when the windows

open. The length of the line at 10 am. The length of the line at 11 am. The rate at which the line is growing in length at

10 am. The time at which the length of the line is a

maximum. The length of time a person who arrives at 9:00

am has to stand in line. The time at which the line disappears.

7.3

Page 9: MATH 152 Applied Calculus Slides may change. Estimate 5.2

U.S. Age DistributionU.S. Age Distribution

Note width of “bin” − 20 yearsNote width of “bin” − 20 years

8.1

Page 10: MATH 152 Applied Calculus Slides may change. Estimate 5.2

U.S. Age DistributionU.S. Age Distribution

Note width of “bin” − 10 yearsNote width of “bin” − 10 years

8.1

Page 11: MATH 152 Applied Calculus Slides may change. Estimate 5.2

HW 2

Math 152 HW Week 2

0

1

2

3

4

5

6

7

8

30 35 40 45 50 55 60 65 70 75 80 85 90 95 100M

ore

HW Score

Fre

qu

ency

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

8.1

Page 12: MATH 152 Applied Calculus Slides may change. Estimate 5.2

HW 3

Math 152 HW 3

0

1

2

3

4

5

35 40 45 50 55 60 65 70 75 80 85 90 95 100M

ore

HW Score

Fre

qu

ency

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

8.1

Page 13: MATH 152 Applied Calculus Slides may change. Estimate 5.2

Normal Distribution8.3

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9.1

Page 15: MATH 152 Applied Calculus Slides may change. Estimate 5.2

9.2

Page 16: MATH 152 Applied Calculus Slides may change. Estimate 5.2

9.2

Page 17: MATH 152 Applied Calculus Slides may change. Estimate 5.2

9.2

Atmospheric pressure

Page 18: MATH 152 Applied Calculus Slides may change. Estimate 5.2

Isobars9.2 Wednesday 2/23/11

Page 19: MATH 152 Applied Calculus Slides may change. Estimate 5.2

Isobars9.2 Forecast for Sunday 2/27/11

Page 20: MATH 152 Applied Calculus Slides may change. Estimate 5.2

Isotherms

Page 21: MATH 152 Applied Calculus Slides may change. Estimate 5.2

Species Density of Birds9.2

Page 22: MATH 152 Applied Calculus Slides may change. Estimate 5.2

9.2

Page 23: MATH 152 Applied Calculus Slides may change. Estimate 5.2

9.2

Page 24: MATH 152 Applied Calculus Slides may change. Estimate 5.2

9.2Revenue from Airline Tickets

Page 25: MATH 152 Applied Calculus Slides may change. Estimate 5.2

9.3

Page 26: MATH 152 Applied Calculus Slides may change. Estimate 5.2

9.3

Page 27: MATH 152 Applied Calculus Slides may change. Estimate 5.2

34

13

9.3

Page 28: MATH 152 Applied Calculus Slides may change. Estimate 5.2

9.2Revenue from Airline Tickets

3500

yx

R

20011

xy

R

Page 29: MATH 152 Applied Calculus Slides may change. Estimate 5.2

Find Extreme Points