7 Chapter Review. FREQUENTLY ASKED Questions. Aid

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1 7 Chapter Review FREQUENTLY ASKED Questions Stud Aid See Lesson Stud 1 Aid ln log 3 See Lesson 7., Eamples 1 and. Tr Chapter Review Question 9. Q: How are the functions 5 log and 5 ln similar and how do the differ? A: Both are logarithmic functions, but the have different bases. The base of 5 log is 1. This is called the common logarithm. The base of 5 ln or 5 log e is e. This is called the natural logarithm. Both functions share the same characteristics: one -intercept at 5 1 no -intercept the graph etends from quadrant IV to quadrant I the domain is restricted, 5., [ R the range is not restricted, 5 [ R Q: How can ou predict the characteristics of a logarithmic function from its equation? A: A logarithmic function of the form 5 a log or 5 a ln has the following characteristics: There is one -intercept, 5 1. There is no -intercept. The value of a indicates whether the graph of the function is increasing or decreasing and determines the function s end behaviour. - The graph is increasing when a.. The graph etends from quadrant IV to quadrant I. - The graph is decreasing when a,. The graph etends from quadrant I to quadrant IV. For eample: 5 log 5 log Chapter 7 Eponential and Logarithmic Functions

2 Q: To perform a logarithmic regression on a data set, how do ou decide which variable is the independent variable? A: Start b considering the contet in which the data set is presented. Use the quantities in the contet to help ou decide which quantit depends on the other. This quantit is the dependent variable, while the other quantit is the independent variable. Stud Aid See Lesson 7.5, Eamples 1 and. Tr Chapter Review Question 11. If ou can t decide from the contet, create a scatter plot of the data. If ou have chosen the independent variable correctl, ou should see either an increasing or decreasing trend, with man points scattered near the -ais. These are characteristics of a logarithmic function. If man points are scattered near the -ais, then ou have incorrectl chosen the independent variable. Switch the variables, and tr again. For eample, the data below shows what happens when ou create a scatter plot with either a or b as the independent variable. Notice that man points are scattered near the -ais in the second scatter plot. To perform a logarithmic regression, b must be treated as the independent variable. a b Scatter plot for a as the independent variable Scatter plot for b as the independent variable 5 b 1 a a b Chapter Review 53

3 PRACTISING Lesson a) Describe how the end behaviour of eponential functions of the form 5 a1b, where a., b., and b 1, differs from the end behaviour of polnomial functions of degree # 3. b) What characteristics do all eponential functions of the form stated in part a) have in common? ii) Lesson 7.. a) Use the equation of this function to predict the characteristics of its graph: 5 9a 1 3 b b) What could ou change in the parameters of the equation to make the function an increasing function? Eplain. 3. For each function, state: i) the -intercepts ii) the -intercept iii) its end behaviour iv) the domain and range v) whether the function is increasing or decreasing a) c) 5 13 b) d) Match each function to its corresponding graph. Provide our reasoning. a) 5 51 b) 5 a 1 3 b Lesson On August 1, 189, gold was discovered near Dawson Cit, Yukon Territor. The population of Dawson Cit eperienced rapid growth after the discover. Below is population data from April 189 to Januar Date Dawson Cit Population April 1, Jul 1, October 1, Januar 1, a) Determine the equation of the eponential regression function models the population growth. b) State the domain and range in this contet. c) Estimate the population of Dawson Cit in mid-ma and in mid-august of 189. Eplain how ou determined our answers. i) Dawson Cit is situated at the junction of the Dawson and Klondike rivers. 5 Chapter 7 Eponential and Logarithmic Functions

4 . Since 5, a naturalist group has been tracking the deer population near the town of Hudson Ba, Saskatchewan. Years After 5 Deer Population a) Construct a scatter plot for the data. b) Determine the equation of the eponential regression function that models the data. c) Assuming the same growth rate, predict the deer population 1 ears after 5. d) In which ear would ou epect the population to have doubled? a) Based on their eperience, the archeologists guessed that the tools were about 8 ears old. If their guess was accurate, what percent of the initial carbon-1 would be present in the tools? b) The tools were found to have 1% of the original carbon-1 present. Determine the age of the tools to the nearest hundred ears. Lesson For the logarithmic function shown below, state the -intercept, the number of -intercepts, the end behaviour, the domain, and the range. 1.5 log A Saskatchewan mule deer 7. Spears and wooden tools used b earl inhabitants were found at an archeological dig site close to Cpress Hills, Alberta. Carbon-1 dating was used to determine the age of the tools. The function that models the deca of carbon-1 is A1t 5 1a 1 b t Predict the -intercept, the number of -intercepts, the end behaviour, the domain, and the range of each function, based on its equation. Verif our predictions using graphing technolog. a) 5 9 log b) 5 log c) 5 1 ln d) 5.3 ln where the initial amount of carbon-1 is 1%, A(t) represents the percent of carbon-1 left in the tools, and t represents the time in ears. Chapter Review 55

5 1. Match each function with its corresponding graph. Provide our reasoning. i) 5 log iii) 5 7 log ii) 5 1 iv) 5 a 3 b a) b) c) Lesson The euphotic zone is the upper m laer in an ocean. Ver little sunlight penetrates deeper than m, so most plants live in the euphotic zone. As a result, 7% of all photosnthesis on Earth occurs in the euphotic zone of the oceans. The table below shows light penetration data for a location in the Pacific Ocean. Depth (m) Penetration of Sunlight (%) Use the equation of the logarithmic regression function to determine the amount of sunlight that penetrates to a depth of m at this location. Epress our answer to the nearest hundredth of a percent. d) Chapter 7 Eponential and Logarithmic Functions