Math 30-2 Exponential and Logarithmic Function Help -multiple questions

Name: ID: A 8. (1 point) A scatter plot is drawn using a data set. Identify the equation of the curve of best fit. 6+ A. y = 8.5 + log x B. y = 8.5 + In x C. y = 8.5 log x D. y = 8.5 In x 9. (1 point Which logarithmic equation correctly represents the exponential equation 107 = x? A. x = log 7 B. x = log 10 C. 7 = log x D. 10 = log x 4Name: ID: A 10. (1 point) Estimate the value of y in the exponential equation 500 = 10'. A. 2.7 B. 2.2 C. 2.9 D. 3.3 11. (1 point) Use the following information to answer the next question. One common irrational number is TE. Another irrational number is called the Euler number and it is represented by e. The value of e is approximately 2.7. If one of the graphs is the graph of y = ex, then it can only be A. graph A C. graph C B. graph B D. none of the graphs Name: ID: A 12. (1 point) The expression y = log 1 x is equivalent to: A. x = C. y = (c) -* B. y = - D. x = logy 13. (1 point) What is the equation of the inverse of the exponential function y = 6x A. X = 10g6 y C. y = 10gx6 B. y = 10g6 X D. y = 10gx7 14. (1 point) Emily used her graphing calculator to draw the graph of the exponential function below. The function she drew was most likely V Set -S x A. y = 4(5) * C. y = z B. y = 3 D. y = 4- 6Name: ID: A Numeric Response 1. (1 point) Use exponential regression to extrapolate the value of y when x = 6. Round your answer to the nearest whole number. X -2 0 2 3 y 77 65 56 47 40 34 Record your answer in the numerical response box from left to right.) 2. (1 point) The fish population in Loon Lake is modelled by the equation P(t) = 2500(0.92) where P(t) represents the number of fish and t represents the time, in years, since January 2010. In which year will the fish population decrease to 2000? (Record your answer in the numerical response box from left to right.) 7Name: ID: A 3. (1 point) A biology laboratory starts a Petri dish with 1000 bacteria. After 30.0 hours, the population is 7250. Determine the doubling time of the bacteria to the nearest tenth of an hour. The doubling-time equation IS t A = A 0 (2) E Where A represents the population after a period of time, A0 represents the initial population, t represents the time, and 517 represents the time it takes for the population to double. (Recordyour answer in the numerical response box from left :0 right.) Problem 1. (4 points) Which exponential function matches each graph below? Provide your reasoning. i)y=2(3)x iii)y=3[l]x 2 ii) y = 3(2)x iV) y = % (3);: a) b) Name: ID: A 2. (4 points) An increasing exponential function y = a(b)" and a decreasing exponential function y = c(d)x intersect at the point (0, 3). a) Which characteristics of the functions are the same? Which characteristics would be different? b) Write the equations of two possible functions. Explain how you chose your functions. 3. (6 points) The followin- data table shows the amount of caffeine in B un_'s s stem after drinking a can of cola. 3) Create a scatter plot, and find curve of best fit for the data using exponential regression. (Find the equation and write it down.) b) Use your line of best fit to determine how much caffeine was in the can, to the nearest tenth. Explain. c) Use your graph to estimate how many minutes it took for the level of caffeine to reach 50 mg. Name: ID: A 4. (4 points) Which function matches each graph below? Provide your reasoning. i) y = - Inx iii) y = -2 logx 2 ii) y = 5logx iv) y = 2(5) * a) b) 5. (6 points) The population of frogs in a marsh was recorded for several years. Year 1 2 3 4 6 7 8 Number of Frogs 252 272 284 290 304 308 312 a) Use logarithmic regression to model the data. (Find the equation and write it down. ) Round all values to the nearest hundredth. b) Estimate the frog population in the 5th year. Show your work. c) Estimate the frog population in the 12th year. Show your work. 6. (1 point) Write x = 1035 as a logarithmic equation. 10Name: ID: A 7. (6 points) Nuclear medicine is a branch of medicine which uses radioactive materials in diagnosis and therapy. Radioactive substances are administered to patients and the radiation emitted is measured. Iodine-131 which has a half-life of k days is a substance that is used to diagnose and treat cancers of the thyroid gland. The graph below is an exponential decay for a dose (D) of iodine-131 given to a patient as a function of time (t) in days. 1001 90 80 70 in body (% of dose) Iodine remaining 30 20 (24, 12.5) 10 10 15 20 25 30 35 40 45 50 55 60 Time (days) a) Explain the significance of the y-intercept of this graph. (1 mark) b) The equation of this graph can be written in the form D = D.(b)* . Using the point (24, 12.5) write the equation and determine the half-life k of iodine-131. (hint: solve graphically or use common logarithms) (3 marks) 1 1