Excel in MATH 1101 through examples
Inessa Levi, September 17, 2013
1. Tables, Graphs, Rate of Change on an Interval, Limiting Behavior
Example: The height h = h(t) of some plants as a function of time t closely follows a logistic formula. For a certain variety of sunflower growing under ideal conditions, and starting at a time when the plant is already a few centimeters tall, its height may be given by the function
where h is measured in centimeters, and t is measured in days.
a) Make a graph of h versus t and describe the behavior of the graph.
b) Calculate the rate of change of h when t increases from 0 to 50 and 50 to 100. ? (Round your answer to two decimal places.)
c) Estimate the maximum height of sunflowers.
2. Approximate Numerical Solution of equations
Example: The temperature C of a fresh cup of coffee t minutes after it is poured is given by
C = 125e-0.03t +73 degrees Fahrenheit.
a) The coffee is cool enough to drink when its temperature is 145 degrees. When will the coffee be cool enough to drink? (Round your answer to two decimal places.)
b) What is the temperature of the coffee in the pot? (Note: We are assuming that the coffee pot is being kept hot and is the same temperature as the cup of coffee when it was poured. Round your answer to the nearest degree.)
c) What is the temperature in the room where you are drinking the coffee? (Hint: If the coffee is left to cool a long time, it will reach room temperature. Round your answer to the nearest degree.)
3. Linear Regression
Example: The following table gives the amount spent on cellular service.
(a) Plot the data points. (Let t be the number of years since 2005 and C the amount of cellular service revenue, in billions of dollars.)
(b) Find the equation of the regression line. (Let t be the number of years since 2005 and C the amount of cellular service revenue, in billions of dollars. Round the regression line parameters to two decimal places.)
(c) In 2009, $152.6 billion was spent on cellular service. If you had been a financial strategist in 2008 with only the data in the table above available, what would have been your prediction for the amount spent on cellular service in 2009? (Round your answer to one decimal place.)
Date / Cellular service revenue C (in billions)2005 / 113.5
2006 / 125.5
2007 / 138.9
2008 / 148.1
4. Exponential Regression:
Example: The data below give the national healthcare costs H, measured in billions of dollars:
Date / Cost H in billions1970 / 75
1980 / 253
1990 / 714
2000 / 1353
2010 / 2570
(a) Plot the data. (Let t be years since 1970 and H the costs in billions of dollars.)
(b) Find an exponential function that approximates the data for health care costs. (Let t be years since 1970 and H the costs in billions of dollars.)
(c) By what percent per year were national health care costs increasing during the period from 1970 through 2010? (Use the model found in part (b). Round your answer to one decimal place.)
(d) Use functional notation to express how much money was spent on health care in the year 2012. (Let t be years since 1970.) Estimate that value. (Use the model found in part (b). Round your answer to the nearest integer.)
(e) From your model, when did health expenditures reach 1000 billion dollars (i.e. 1 trillion dollars)?
(f) Use functional notation to express how much money was spent on health care in the year 2060. (Let t be years since 1970.) Estimate that value. (Use the model found in part (b). Round your answer to the nearest integer.) The actual expenditures in 1960 were 27 billion dollars. Did the trend in the model hold as early as 1960?
Note: In 2012 survey of my sections of MATH 1101 (90% response rate)
89% used Excel to do their work; and 90% of all respondents believed Excel to be useful ( not necessarily the same students);98% of those who used Excel found it useful.