Pre Calculus Midterm Exam Score Name 569454

Pre Calculus Midterm Examscore Name

Pre-Calculus Midterm Exam Score: ______ / ______ Name: ____________________________ Student Number: ___________________ Short Answer: Type your answer below each question. Show your work. 1 Verify the identity. Show your work. cot θ ∙ sec θ = csc θ 2 A gas company has the following rate schedule for natural gas usage in single-family residences: Monthly service charge $8.80 Per therm service charge 1st 25 therms $0.6686/therm Over 25 therms $0.85870/therm What is the charge for using 25 therms in one month? Show your work. What is the charge for using 45 therms in one month? Show your work. Construct a function that gives the monthly charge C for x therms of gas. 3 The wind chill factor represents the equivalent air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is W(t) = where v represents the wind speed (in meters per second) and t represents the air temperature . Compute the wind chill for an air temperature of 15°C and a wind speed of 12 meters per second. (Round the answer to one decimal place.) Show your work. 4 Complete the following: (a) Use the Leading Coefficient Test to determine the graph's end behavior. (b) Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept. Show your work. (c) Find the y-intercept. Show your work. f(x) = x2(x + 2) (a). (b). (c). 5 For the data set shown by the table, a. Create a scatter plot for the data. (You do not need to submit the scatter plot) b. Use the scatter plot to determine whether an exponential function or a logarithmic function is the best choice for modeling the data. Number of Homes Built in a Town by Year 6 Verify the identity. Show your work. (1 + tan2u)(1 - sin2u) = Verify the identity . Show your work. cot2x + csc2x = 2csc2x - Verify the identity. Show your work. 1 + sec2xsin2x = sec2x 9 Verify the identity. Show your work. cos(α - β) - cos(α + β) = 2 sin α sin β 10 The following data represents the normal monthly precipitation for a certain city. Draw a scatter diagram of the data for one period. (You do not need to submit the scatter diagram). Find the sinusoidal function of the form that fits the data. Show your work. . 11. The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the graph to answer the question. Does the graph represent a function? Explain 12. Find the vertical asymptotes, if any, of the graph of the rational function. Show your work. f(x) = 13. The formula A = 118e0.024t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 140 thousand? Show your work. 14. Find the specified vector or scalar. Show your work. u = -4i + 1j and v = 4i + 1j; Find . 15. Find the exact value of the trigonometric function. Do not use a calculator. 16. Find the x-intercepts (if any) for the graph of the quadratic function. 6x2 + 12x + 5 = 0 Give your answers in exact form. Show your work. 17. Use the compound interest formulas A = Pert and A = P to solve. Suppose that you have $11,000 to invest. Which investment yields the greater return over 10 years: 6.25% compounded continuously or 6.3% compounded semiannually? Show your work. 18. Find functions f and g so that h(x) = (f ∘ g)(x). h(x) = (6x - . Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to describe the graph the given function. h(x) = 2 | x | + . Find the reference angle for the given angle. Show your work. -404° Score: ______ / ______ H03 Quiz #2 February 12/13, 2015 Name: Problem Section: [30 marks] Student #: Question #1: [6 marks] Consider a small open economy macro model at full-employment with Y = 4000. Assume that the domestic price as well as foreign price stays constant at one. Y = C + I + G + NX C = 200 + 0.8(Y – T) [Autonomous consumption = 200] T = 1000 G = 1000 I = 800 – 100r [Autonomous investment = 800] World interest rate = r = 4 NX = e [Autonomous net export is 500] Find the following: [ Each numerical answer is 0.5 marks ] (a) Exchange rate (e) = S – I = (b) Increase G from 1000 to 1200. Exchange rate (e) = S – I = (c) Increase both G from 1000 to 1200 and increase T from 1000 to 1200. Exchange rate (e) = S – I = (d) [4 marks] Assume full-employment Y. Assume that both SG and NX are zero at the initial equilibrium. Assume further that SP is not a function of interest rate. Assume that the domestic price = world-price = 1 Fill in the box with any of the following three signs. ( = increase ( = decrease 0 = no change Each box is worth 0.25 marks Causes e NX C SP SG S I S -I Higher autonomous tax Higher autonomous investment Question #2: [3 marks] (a) Economy’s output function is Y = L0.8K0.2 Output per labour function is y = (K/L)0.2 = k0.2 Assume that ∆L/L is 4 percent and ∆K/K is 2 percent. Find the following: Growth of labour-productivity = (b) Economy’s output function is Y = L0.8K0.2 Output per labour function is y = (K/L)0.2 = k0.2 Assume that ∆L/L is 4 percent and ∆K/K is 4 percent. Find the following: Growth of labour-productivity = (c) Economy’s output function is Y = L0.8K0.2 Output per labour function is y = (K/L)0.2 = k0.2 Assume that ∆L/L is 4 percent and ∆K/K is 8 percent. Find the following: Growth of labour-productivity = Question #3: [11 marks] Each numerical answer is worth 0.5 marks (a) Consider an economy with the following demand and supply function of capital. K = 120 – R [Demand function] K = R [Initial supply function] K = 3R [New supply function due to higher fiscal savings] (i) Initial labour income in a closed model = New labour income in a closed model = (ii) Assume a small open macro model with world interest rate = R = 30 Initial labour income = Initial domestic capital income = Initial GNP = Initial GDP = Capital inflow = Initial labour-income/GNP ratio = New GNP = New GDP = Capital inflow = New labour-income/GNP ratio = (iii) Assume a small open macro model with world interest rate = R = 50 Initial labour income = Initial domestic capital income = Initial GNP = Initial GDP = Capital inflow = Initial labour-income/GNP ratio = New GNP = New GDP = Capital outflow = New labour-income/GNP ratio = Question #3: [6 marks] Each numerical answer is worth 0.5 marks Consider Solow growth model with output per labour function of y = k0.5 (i) Assume that the saving rate (s) is 0.2 and (δ + n+ g) is 0.1 Find the steady-state solutions of the following: y = k = sy = i = c = (ii) Assume that the saving rate (s) is 0.5 and (δ + n+ g) is 0.1 Find the steady-state solutions of the following: y = k = sy = i = c = (iii) Assume that the saving rate (s) is 0.8 and (δ + n+ g) is 0.1 y = k = sy = i = c = 35 True-False Questions: [70 marks] Use scan sheet for True-False Questions. Bubble A is the statement is True and Bubble B if the statement is false. Questions #1-8 are based on a small open economy full-employment macro model. 1. If large countries (for example, USA) increase government spending, it will lead to higher world interest rate (r). As a result, small economy’s investment as well as NX will decrease. 2. Higher autonomous investment in a small economy will lead to higher investment (I), higher value of domestic currency (e) and lower net export (NX). 3. Imposition of new tariff will lead to, higher e and lower NX. 4. Assume that MPC is 0.8 and MPS is 0.2. If both G and T increase by 100, NX will decrease by 20. 5. If a large economy (for example, USA) experiences a rightward shift of their investment function, spending, it will lead to higher r, higher e and lower NX. 6. Higher G will lead to higher r. As a result, small open economy’s (S – I) will increase, its capital outflow will increase, e will decrease and its NX will increase. 7. Lower government expenditure will lead to higher net capital inflow, higher e and lower next export. 8. Increase in the popularity of foreign cars will increase e in such a way that NX at the end will remain unchanged. 9. Long-run purchasing power parity (in other words, real exchange rate in the long-run remains constant) implies that if the differential between domestic inflation and foreign inflation is 5%, then the nominal exchange rate (e) of domestic currency will depreciate by approximately 5%. 10. Assume that small economy’s inflation rate exceeds world inflation rate by 2 percent, but nominal exchange rate remains constant. As a result, the real exchange rate will increase by 2 percent and small economy’s NX will decline. 11. If the unemployment rate is 8 percent and if the number of unemployed workers is 120 thousand, then the number of employed workers is 1380 thousand. 12. The growth of output at steady-state y is zero. 13. Higher the population growth, lower the k and lower the steady-state y. Answer Questions # on the basis of following labour market data for a given period in an economy. Labour Force = L = E + U = 1500 thousand workers Job-finding rate = f = 0.46 Job-separation rate = s = 0.04 fU = sE [Steady-state condition] 14. Steady-state unemployment rate is 10 percent. 15. Number of workers losing jobs = Number of workers finding jobs =50 thousand Answer Questions #16-19 on the basis of small open economy macro model. Consider a small open economy macro model at full-employment with Y = 5000. Assume that the domestic price as well as foreign price stays constant at one. Y = C + I + G + NX C = 600 + 0.6(Y – T) [Autonomous consumption = 600] T = 1000 G = 1000 I = 1200 – 50r [Autonomous investment = 1200] World interest rate = r = 4 NX = e [where autonomous net export is 500] 16. The equilibrium e is 1 and NX is zero. 17. If T decreases by 10, then NX will decrease by 4 18. Consider the original model. Assume that autonomous investment increases by 100. As a result, e will increase to 1.2 and NX will decrease by . Consider the original model. Assume that autonomous net export increases by 100 (due to import quota) and the NX function becomes NX= 600 – 500e. As a result, e will increase to 1.2, but NX will increase eventually.. 20. Rightward shift of the labour demand curve can be caused by the following: · More capital per labour · Lower payroll taxes · Higher level of skill and human capital per labour 21. Assume that the unskilled workers experience higher labour-productivity due to government spending on labour-training programs. As a result, the structural unemployment rate will decline. 22. Cuts in payroll taxes will bring more after-tax revenues to employers. As a result, the demand curve for labour will shift the right and structural unemployment rate will go down in an economy. 23. Higher union wage will lead to higher frictional unemployment rate. 24. If the job-separation rate (s) is increases, unemployment rate decreases. 25. If Okun’s Law is true, the steady-state unemployment rate is zero. 26. Higher cyclical unemployment due to recession is caused by higher Minimum Wages. Answer Questions #27-30 on the basis of the following: y = k1/2 [y is the output or income per labour] In the above equation, y stands for output and k for capital per labour Assume that y = k1/2, s = 0.3 and δ = 0.1. Assume that the population growth rate is zero along with zero technological change. 27. The steady-state y is 3 and consumption per labour is 2. 28. If marginal propensity to save (mps) increases to 0.8, while δ remains at 0.1, then steady-state y will increase to 8 and steady-state saving per labour will be 6. 29. The Golden Rule MPk is 0.1. The Golden Rule y and Golden Rule c are 5 and 2.5, respectively. 30. The Golden Rule marginal propensity to save is 0.5. 31. Consider Solow growth model with zero population growth and no technological change. If saving per labour is less than depreciation cost of k per labour, then the capital stock will decrease and output will decrease until the steady state y is attained where sy = depreciation costs per labour 32. Consider an economy with the production function of Y = AL0.8K0.2, where Y is output, A is technology, L is labour and K is capital. If the output-growth rate is 8%, labour-growth rate is 5% and capital-growth rate is 5%, the growth of total factor-productivity (or Solow residual) is 3%. 32. If two economies are identical in all respects, but one country has higher population growth rate. The country with higher population will have lower capital labour-ratio and lower income per labour. 33. Consider Solow growth model with zero population growth rate and zero technological change. Further assume that country A has higher mpc than that of country B. We can conclude that the country A will have higher y than that of country B. 34. Higher the steady-state saving per labour, higher is the steady-state y. 35. In Solow model, the MPk at 4th unit of k is higher than the MPk at 3rd unit of k.