11. The table shows the temperature of coffee (in Fahrenheit) as a function of the number of minutes since the coffee was poured from the pot into a cup. Temp (*F) 179.5 168.7 158.1 149.2 a. Graph the data on your calculator. Why is an exponential function a better fit for the data than a linear function? Time (mins) 11 15 141.7 134.6 125.4 18 22 25 b. Find the exponential regression equation for the data Round decimals to 4 places. 123.5 116.3 30 34 113.2 109.1 105.7 102.2 100.5 38 42 45 50 c. Compare the y-intercept of the regression equation you found to the corresponding real data value. How close are these values?

11. The table shows the temperature of coffee (in Fahrenheit) as a function of the number of minutes since the coffee was poured from the pot into a cup. Temp (*F) 179.5 168.7 158.1 149.2 a. Graph the data on your calculator. Why is an exponential function a better fit for the data than a linear function? Time (mins) 11 15 141.7 134.6 125.4 18 22 25 b. Find the exponential regression equation for the data Round decimals to 4 places. 123.5 116.3 30 34 113.2 109.1 105.7 102.2 100.5 38 42 45 50 c. Compare the y-intercept of the regression equation you found to the corresponding real data value. How close are these values?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Question

11. The table shows the temperature of coffee (in Fahrenheit) as a function of the number
of minutes since the coffee was poured from the pot into a cup.
a. Graph the data on your calculator. Why is an exponential function a
better fit for the data than a linear function?
Temp
(*F)
179.5
Time (mins)
5
168.7
8
158.1
11
149.2
15
141.7
18
134.6
22
125.4
123.5
116.3
113.2
109.1
105.7
102.2
100.5
25
b. Find the exponential regression equation for the data
Round decimals to 4 places.
30
34
38
42
45
50
c. Compare the y-intercept of the regression equation you found to the corresponding real data value. How close are these values?
d. Use the regression equation to predict the temperature of the coffee after an hour.
e. Graph the regression equation on your calculator. Create a window that has an XMAX of at least 420 (that's 7 hours!). TRACE on
the graph to find the temperature of the function after 420 minutes. What is the temperature? Explain why using the function to
model the temperature after this many hours are not reasonable.

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