[answered] MATH 153 UNIT 3 PROJECT A Project is Due Tuesday December 2

Hello Peter? --You've helped me before. I have another math?project that I'm having some trouble with.

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MATH 153

 

UNIT 3 PROJECT A

 

Project is Due Tuesday December 20. Projects turned in by 5:00 PM Thursday December 15th

 

will receive 5 points extra credit.

 

1. You will find the equation of an exponential function through two points in two different ways.

 

(points)

 

(5) a. Find the exponential function of the form y ae kx that goes through the points

 

(0, 6) and (2, 8). Show all your steps and use four decimal places. Write a complete

 

answer.

 

(5) b. Use your graphing calculator to enter your exponential function into Y1 and construct an

 

input/output table for inputs of x = 2, 1, 0, 1, 2. (5) c. Extend the table by entering ln(y1) into Y2. Provide a printout of this extended table.

 

(You may take a picture with your phone and upload it into the project.) Label the

 

columns x, y, and ln(y). (5) d. Do the ordered pairs (x, ln(y)) form a linear or exponential function? Justify your answer. (5) e. Find a possible formula for ln(y) as a function of x, using the values from the table in

 

part c. Show your work. (5) f. Solve your formula for y. (5) g. Write your answer in the form y aekx showing all steps and compare your answer to

 

part a. 5/14

 

2. (32 points) You have a total of 860 feet of fencing to enclose a large rectangular area and

 

divide it into four smaller pens of the same dimensions. The fencing used to divide the large pen

 

must be parallel to the same side of the large rectangle, as shown below. Your goal is to

 

maximize the total rectangular area. Give the dimensions as well as the maximum area. Show

 

your steps leading up to the final answer. Problem 3 (13 Points): Complete Problem 2 and 3 from Webassign Homework Fitting

 

Curves to Data Homework . If you did these in webassign I will give you the points

 

awarded for those two problems. If you are not doing webassign, then do the following

 

problems in the book

 

Page 398 #4 and the problem on the next page. Print out and hand in. 5/14

 

The U.S. health-care expenditures for 1970?2008 are given in the table below, and

 

a scatter plot of the data is shown in the figure.

 

Year Health-care expenditures

 

(in billions of dollars) 1970 74.3 1980 251.1 1985 434.5 1987 506.2 1990 696.6 1992 820.3 1994 937.2 1996 1039.4 1998 1150.0 2000 1310.0 2001 1424.5 2008 2339.5 (a) Does the scatter plot shown suggest an exponential model? (b) Make a table of the values (t, ln E) and a scatter plot, where t is the number of years 5/14

 

since 1970 and E is health-care expenditures in billions of dollars. (Round your answers to

 

five decimal places.) Does the scatter plot appear to be linear? 5/14 (c) Find the regression line for the data in part (b). Choose 1

 

ln(E) = 0.088 + 4.619t

 

ln(E) = 2.309 + 0.176t

 

ln(E) = 0.044 + 9.237t

 

ln(E) = 4.619 + 0.088t

 

ln(E) = 0.088e2.309t (d) Use the results of part (c) to find an exponential model for the growth of health-care

 

expenditures. Choose 1

 

E(t) = 101.353 + 0.044t

 

E(t) = 202.707e0.044t

 

E(t) = 0.176e50.677t

 

E(t) = 101.353e0.088t

 

E(t) = 0.088e101.353t

 

(e) Use your model to predict the total health-care expenditures in 2016. (Round your

 

answers to two decimal places.) (c) If the light intensity drops below 0.05 lumen (lm), a certain species of algae can't survive

 

because photosynthesis is impossible. Use your model from part (a) to determine the depth

 

below which there is insufficient light to support this algae. (Round your answer to two

 

decimal places.)

 

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