Exponential and Logarithmic Functions Unit Test 15/12/15 20:11 Exponential and Logarithmic Functions Unit Test Frank Gjurashaj is taking this assessment. Multiple Choice 1. Which graph best represents y = 2x + 1? (1 point) https://www.connexus.com/content/render.aspx?disableAssessm…er=1393561&page=1&header=true&idUnit=30171&idLesson=340062 Page 1 of 14 Exponential and Logarithmic Functions Unit Test 15/12/15 20:11 2. Some investments in the stock market have earned 10% annually. At this rate, earnings can be (1 point) found using the formula , where A is the total value of the investment, P is the initial value of the investment, and n is the number of years the money is invested. If $1,500 is invested in the stock market at this annual rate of return, what is the expected total value after 18 years? $29,700.00 $28,050.00 $8,339.88 $7,581.71 3. The pH of a liquid is a measure of how acidic or basic it is. The concentration of hydrogen ions in a liquid is labeled [H+]. Use the formula pH = –log[H+] to find the pH level, to the nearest tenth, of a liquid with [H+] about 4.3 × 10-14. (1 point) 13.4 14.6 –13.4 –14.6 4. Graph the logarithmic function. (1 point) y = log(x – 3) https://www.connexus.com/content/render.aspx?disableAssessm…er=1393561&page=1&header=true&idUnit=30171&idLesson=340062 Page 2 of 14 Exponential and Logarithmic Functions Unit Test https://www.connexus.com/content/render.aspx?disableAssessm…er=1393561&page=1&header=true&idUnit=30171&idLesson=340062 15/12/15 20:11 Page 3 of 14 Exponential and Logarithmic Functions Unit Test https://www.connexus.com/content/render.aspx?disableAssessm…er=1393561&page=1&header=true&idUnit=30171&idLesson=340062 15/12/15 20:11 Page 4 of 14 Exponential and Logarithmic Functions Unit Test 15/12/15 20:11 5. Expand the logarithmic expression. (1 point) 6. What is the value of log648? (1 point) 3 2 7. Solve the exponential equation. (1 point) 1258x–2 = 150 –0.1203 0.3797 https://www.connexus.com/content/render.aspx?disableAssessm…er=1393561&page=1&header=true&idUnit=30171&idLesson=340062 Page 5 of 14 Exponential and Logarithmic Functions Unit Test 15/12/15 20:11 0.3705 2.1297 8. Solve log(2x + 3) = 3. (1 point) 500 997 9. Solve the equation. (1 point) log(x + 5) – logx = 3 0.0505 0.0050 2.5 199.8 10. What is the percent rate of change in function y = (0.96)x? Determine whether the function represents exponential growth or exponential decay. (1 point) 4%; exponential decay 4%; exponential growth 0.4%; exponential growth 0.04%; exponential decay 11. Use natural logarithms to solve the equation. Round to the nearest thousandth. (1 point) 3e2x+ 5 = 27 1.9924 0.9962 1.5455 0.4327 12. Write the expression as a single logarithm. (1 point) 5logby + 4logbx logb(y5 + x4) logb(y5x4) (5 + 4) logb(y + x) https://www.connexus.com/content/render.aspx?disableAssessm…er=1393561&page=1&header=true&idUnit=30171&idLesson=340062 Page 6 of 14 Exponential and Logarithmic Functions Unit Test 15/12/15 20:11 logb(yx5 + 4) 13. The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years. (2 points) Write an exponential function for the graph. Use the function to find the value of the boat after 9.5 years. https://www.connexus.com/content/render.aspx?disableAssessm…er=1393561&page=1&header=true&idUnit=30171&idLesson=340062 Page 7 of 14 Exponential and Logarithmic Functions Unit Test Select attachment 15/12/15 20:11 or drag and drop a file into this area - 20 MB limit 14. Write the equation in logarithmic form. (2 points) https://www.connexus.com/content/render.aspx?disableAssessm…er=1393561&page=1&header=true&idUnit=30171&idLesson=340062 Page 8 of 14 Exponential and Logarithmic Functions Unit Test Select attachment 15/12/15 20:11 or drag and drop a file into this area - 20 MB limit 15. Evaluate the logarithm. (2 points) log749 https://www.connexus.com/content/render.aspx?disableAssessm…er=1393561&page=1&header=true&idUnit=30171&idLesson=340062 Page 9 of 14 Exponential and Logarithmic Functions Unit Test Select attachment 15/12/15 20:11 or drag and drop a file into this area - 20 MB limit 16. Solve ln 2 + ln x = 5. Round to the nearest thousandth, if necessary. (2 points) https://www.connexus.com/content/render.aspx?disableAssess…er=1393561&page=1&header=true&idUnit=30171&idLesson=340062 Page 10 of 14 Exponential and Logarithmic Functions Unit Test Select attachment 15/12/15 20:11 or drag and drop a file into this area - 20 MB limit 17. The sales of lawn mowers t years after a particular model is introduced is given by the function y = 5500 ln(9t + 4), where y is the number of mowers sold. How many mowers will be sold 5 years after a model is introduced? Round the answer to the nearest whole number. https://www.connexus.com/content/render.aspx?disableAssess…er=1393561&page=1&header=true&idUnit=30171&idLesson=340062 (2 points) Page 11 of 14 Exponential and Logarithmic Functions Unit Test Select attachment 15/12/15 20:11 or drag and drop a file into this area - 20 MB limit 18. In a particular region of a national park, there are currently 330 deer, and the population is increasing at an annual rate of 11%. (3 points) a. Write an exponential function to model the deer population in terms of the number of years from now. b. Explain what each value in the model represents. c. Predict the number of deer that will be in the region after five years. Show your work. https://www.connexus.com/content/render.aspx?disableAssess…er=1393561&page=1&header=true&idUnit=30171&idLesson=340062 Page 12 of 14 Exponential and Logarithmic Functions Unit Test Select attachment 15/12/15 20:11 or drag and drop a file into this area - 20 MB limit 19. In the equation (2 points) y = ab(x – h) + k, how does the value of k affect the graph? https://www.connexus.com/content/render.aspx?disableAssess…er=1393561&page=1&header=true&idUnit=30171&idLesson=340062 Page 13 of 14 Exponential and Logarithmic Functions Unit Test 20. Without graphing, determine whether the function = (5.2)x represents exponential growth or y exponential decay. Explain why. 15/12/15 20:11 (2 points) © 2015 Connections Education LLC. https://www.connexus.com/content/render.aspx?disableAssess…er=1393561&page=1&header=true&idUnit=30171&idLesson=340062 Page 14 of 14