Math2UU3*TEST3. Duration of Test: 60 minutes McMaster University, 6 November Last name (PLEASE PRINT): First name (PLEASE PRINT): Student No.

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1 Math2UU3*TEST3 Day Class Duration of Test: 60 minutes McMaster University, 6 November 2018 Dr M. Lovrić Last name (PLEASE PRINT): First name (PLEASE PRINT): This test has 8 pages. Calculators allowed: Casio fx991ms or fx991ms PLUS, or similar (i.e., two lines of display and no graphing capabilities). If some piece of information is missing, you must decide on its value. 1. Circle ONE answer, or fill in the blank. No justification is needed. (a)[2] The conversion between degrees Celsius and degrees Fahrenheit is given by the formula F = 9 5 C +32. True/false: Degrees Celsius and degrees Fahrenheit are positively correlated. (A) true (B) false (b)[2] The future amount of some quantity is obtained by removing one-fifth of the present amount. That quantity shows (A) exponential growth (B) linear growth (C) exponential decay (decrease) (D) linear decay (decrease) 1

2 (c)[2] Thinking about climate change - which one of the following quantities has been increasing roughly exponentially in the last 50 years? (A) the average global temperature (B) Arctic sea ice extent (area) (C) the amount of carbon dioxide in the atmosphere (D) the total volume of glacier ice on the Northern Hemisphere (d)[2] The surface area of a ball B is 9 times larger than the surface area of a ball A. This means that the volume of the ball B is of the ball A. times larger than the volume (e)[2]radioactiveisotope Iodine-131 issometimes released (due to malfunction) from nuclear power plants. In one such case, investigators determined that 15 days after the leak occurred, 75% of the initial amount of Iodine-131 was gone (i.e., diffused into air and/or decayed into substances which do not present a threat). Based on this information, the half-life of Iodine-131 is days. 2

3 (f)[2] How long will it take for a quantity Q that grows at 5% per year to increase 10-fold (i.e., how long will it take to grow from Q to 10Q)? (A) About 10 years (B) Less than 40 years (C) About 45 years (D) More than 60 years Questions (g) and (h) refer to the following graph with logarithimc scale for the response variable. log 3.2 A 1.6 E C 0.4 D x 1.6 B (g)[2] Which statement is correct about the values represented by data points E and D? (A) E is twice as large as D (B) E is four times larger than D (C) E is two orders of magnitude larger than D (D) E is four orders of magnitude larger than D (h)[2] Which statement is correct about the values represented by data points A and B? (A) A is positive and B is negative (B) The difference between A and B is about the same as A (C) A is 4.8 times larger than B (D) The difference between A and B is about

4 2. [1] The scatter plot below shows the number of harp seals in a small area between Rankin Inlet and Thomson Island, Nunavut. Your friend is about to compute the exponential regression to describe the given scatter plot, and then use it to extrapolate. You tell them that this is not a good idea. Give a very specific reason which supports your opinion (very specific means related to the data shown, and not a general reason such as extrapolation is never reliable ). 3. (a)[1] The conversion formula between degrees Kelvin and degrees Celsius is given by C = K True/false: The relationship between degrees Kelvin and degrees Celsius is linear. explanation is necessary.) (No (b)[1] The conversion between degrees Celsius and degrees Fahrenheit is given by the formula F = 9 5C +32. Explain what the slope of 9/5 says about the relationship between degrees Celsius and degrees Fahrenheit. 4

5 4. Consider the data and the corresponding regression calculation for the Arctic Sea Ice extent, i.e., the area A covered in ice in late summer. By t we denote time in years, with t = 0 representing the earliest data point. (a)[3] What is the slope of the regression line (round off to three decimal places)? What are its units, and what is its meaning? (b)[2] Extrapolate to find the year when, according to the model, the sea ice will completely disappear. Round off to the nearest integer. 5

6 5. When we drive, our car uses energy (fuel) to combat air resistance. From physics we know that air resistance is proportional to the square of the velocity, and that fuel consumption is proportional to air resistance. (a)[2] Sketch a possible graph showing how fuel consumption depends on the velocity of a car. Label the axes. (b)[1] Use (a) to explain why increasing the velocity from 30 to 40 km/h requires less fuel than increasing the velocity from 90 to 100 km/h (although in both cases the change is 10 km/h). (c)[2] How does fuel consumption at the speed of 25 km/h compare to the fuel consumption at the speed of 75 km/h? Explain your reasoning. 6

7 6. (a)[3] Some strains of E. coli bacteria have a generation time of 20 minutes. Assuming that the bacteria multiply in such a way that no daughter bacteria die (so one bacterium splits into two bacteria and both live), find out the surface area (in metres squared; round off to one decimal place) that the E. coli bacteria would cover in one day. Assume that the initial population is one bacterium. As well, assume that 9 million E. coli bacteria occupy an area of 1 square metre. (b)[2] Total surface area of Earth (land and oceans) is about 510 million km 2. How long would it take for the bacteria to cover the whole Earth - more or less than one day? 7

8 7. (a)[1] Present (2018) population of Earth is about 7.6 billion, and its average annual growth rate is 1.05% (so down from the rate of 1.14% mentioned in lectures). Write a formula that models population growth, i.e., which shows how world population depends on time, measured in years starting from 2018 (so take t = 0 to represent 2018). (b)[1] Present amount of all resources on Earth (food, energy, etc.) has been estimated to be 8 billion resource units. Assuming that the production of resources increases by a constant amount of 0.07 billion resource units per year, write a formula that models the growth of resources (i.e., which shows how resource production depends on time, measured in years starting from 2018). (c)[4] Identify the curves that you obtained in (a) and (b), and sketch their graphs in the same coordinate system (where the vertical axis will represent both the population and the resources). You can do it even if you did not answer (a) and (b). Explain the significance of the graph in (c) for the World population. 8 THE END