11:38 PM Mon Oct 28 3.71% The term "log-normal" gives a clue about how this distribution connects to both logarithms and the normal distribution. Here's how: if your data follows a log-normal distribution, taking the logarithm of each data point will transform the dataset into a normal distribution. In other words, applying the logarithmic transformation to log-normal data results in a set of values that are normally distributed. This relationship helps make it easier to analyze and work with data that has a log-normal pattern. See figure below 0:06 0:04 002 Lognormal Distribution of variable X E(X) 001 Normal Distribution 0.00 of variable Y 40 natural scale so 001 02 03 04 05 06 Relationship between the normal and log-normal function |

11:38 PM Mon Oct 28 3.71% The term "log-normal" gives a clue about how this distribution connects to both logarithms and the normal distribution. Here's how: if your data follows a log-normal distribution, taking the logarithm of each data point will transform the dataset into a normal distribution. In other words, applying the logarithmic transformation to log-normal data results in a set of values that are normally distributed. This relationship helps make it easier to analyze and work with data that has a log-normal pattern. See figure below 0:06 0:04 002 Lognormal Distribution of variable X E(X) 001 Normal Distribution 0.00 of variable Y 40 natural scale so 001 02 03 04 05 06 Relationship between the normal and log-normal function |

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 5SE: What does the y -intercept on the graph of a logistic equation correspond to for a population...

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What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
Table 6 shows the year and the number ofpeople unemployed in a particular city for several years. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the number of unemployed reach 5 people?
The US. import of wine (in hectoliters) for several years is given in Table 5. Determine whether the trend appearslinear. Ifso, and assuming the trend continues, in what year will imports exceed 12,000 hectoliters?
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Planetary Velocity The following table gives the mean velocity of planets in their orbits versus their mean distance from the sun. Note that 1AU astronomical unit is the mean distance from Earth to the sun, abut 93 million miles. Planet d=distance AU v=velocity km/sec Mercury 0.39 47.4 Venus 0.72 35.0 Earth 1.00 29.8 Mars 1.52 24.1 Jupiter 5.20 13.1 Saturn 9.58 9.7 Uranus 19.20 6.8 Neptune 30.05 5.4 Astronomers tell us that it is reasonable to model these data with a power function. a Use power regression to express velocity as a power function of distance from the sun. b Plot the data along with the regression equation. c An asteroid orbits at a mean distance of 3AU from the sun. According to the power model you found in part a, what is the mean orbital velocity of the asteroid?
What situations are best modeled by a logistic equation? Give an example, and state a case for why the example is a good fit.
Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
What type (s) of translation(s), if any, affect the range of a logarithmic function?