Advanced Functions 12 | @ Wiz Kidz



Name : ________________________ MHF4U1 Unit 6: Logarithmic and Exponential FunctionsK/U /26APP /15COM /9TH /11[Type a quote from the document or the summary of an interesting point. You can position the text box anywhere in the document. Use the Text Box Tools tab to change the formatting of the pull quote text box.][Type a quote from the document or the summary of an interesting point. You can position the text box anywhere in the document. Use the Text Box Tools tab to change the formatting of the pull quote text box.][Type a quote from the document or the summary of an interesting point. You can position the text box anywhere in the document. Use the Text Box Tools tab to change the formatting of the pull quote text box.]LIFE LINES First Line Notebook 50/50KNOWLEDGE/UNDERSTANDINGConvert from exponential to logarithmic form(1)128=27Convert from logarithmic to exponential form(1)log749=2Evaluate(CHOOSE 4 of 6…)(4)log6363 b)log 1c) log 1100d) log5125 e)log27f)log218Express each of the following as a logarithm of a product or quotient.a) b) (1, 1)c) d) (2, 2) Use the laws of logarithms to express each of the following as a sum or difference.a) b) (2, 2)c) d) (2, 3)3. Sketch the following function y=-3log 2x-4+1. Properly label each new point following each transformation.(5)APPLICATION1.The stellar magnitude scale compares the brightness of stars using the equation m1-m2=logb1b2. Sirius is the brightest star appearing in our sky, with a magnitude of 1.5. How much brighter does Sirius appear than Neptune, whose apparent magnitude is 0.12.(5)2.The formula to calculate the mass, A, remaining from an original sample of radioactive material with mass A0, is determined using the formula A=A0(1/2)t/p , where t is time and p is the time for half-life to occur. The half-life of a radioactive substance is 4 h. How long will it take for a 325 g sample to decay to 80 g? (5)3.A weaker earthquake has a magnitude of 6.2, and the following day a stronger earthquake occurs with triple the intensity. What is the magnitude of the stronger earthquake?(5)COMMUNICATION 1.Describe how the graph of is related to . (3)2.How would you solve for the letter t in the equation 10=2t?(2)3.Show how a magnitude 7 earthquake is 100 times stronger than a magnitude 5 earthquake.(2)4.How are exponential and logarithmic functions related?(2)THINKING1.State the restrictions (or equation of the vertical asymptote) of the following logarithmic function y=logx+4-1(3)2.Describe how the transformations on the function y=-2 log 2(x-3) are different from the function y=2log-2(x-3).(3)3.When you drink a cup of coffee, the percent P, of caffeine remaining in your bloodstream is related to the elapsed time, t, in hours, by t = 5 (logP/log0.5).(5)a) How long will it take for the amount of caffeine to drop to 20% of the amount consumed?b) Suppose you drink a cup of coffee at 9am. What percent of the caffeine will remain in your body at noon?BONUS QUESTION (+2)A radioactive sample has a half life of 3 years, and has an initial mass of 68g. How long will it take for the sample to lose 8g?OROn March 11, 2011 Japan experienced a tremendous earthquake, measuring 9.0 on the Richter Scale. How much more intense was the 9.0 magnitude earthquake compared to the 7.2 magnitude earthquake which hit Kobe, Japan on Jan 17, 1995? ................
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