\f1. Solve the differential equation y/ = y', y(-5) = -}. Oy= 4-2 Ov=4+7 Ov=4+ ONone of the other answers is correct 2. Solve the differential equation = -5rev, with the initial condition (0, - 1). Oy= 52 Ov= $2 Oy= - In(e + ) Oy= - In(e + 5x) Oy= - In(2) + 10 In() 3. Solve the differential equation y/ = 3y, with y(0) = 6. Oy = 6edx Oy= 2 +18 Oy= 6ln(3x) Oy=-32 +6 Ov=ed +6 4. Which of the following is the solution to the differential equation 4 = 4 with the initial condition y(e) = -5? Oy = 3ln() - 10 Oy = 3 In(x) Oy = 3 In(x) + 8 Oy = 3ln(x) + 10 Oy = 3ln(x) - 8 5. I put a gallon of milk into my refrigerator 1 hour ago. If the inside of the refrigerator is 40"F, and the temperature of the milk has dropped from 49"F to 43"F, what is the rate at which the temperature is dropping after an additional hour? HINT: Newton's Law of Cooling is T = (To - To)e-# + Ta O # = -3In() degrees Fahrenheit / hour O "T - 3 In( ) degrees Fahrenheit / hour O * = - In( }) degrees Fahrenheit / hour O 4 - { In( ) degrees Fahrenheit / hour O # = In( ) degrees Fahrenheit / hour16. A population P grows according to the equation 4 = kP. If the population of P triples every 35 years, what is the value of k? O k = 0.055 O k = 0.039 O k= 0.031 O k = 0.053 O k = 0.044 17. After 28 days, a radioactive substance has decayed to 39.1% of its original amount. After an additional 33 days, what percent of its original amount will it have decayed to? 14.350 12.928 9.696 O 4.098 13.574 18. If the initial population of bacteria in a petri dish is 10,000 and it grows 2% per hour, how long will it take to reach a population of 35,000? 57.001 hours O 80.427 hours O 35.578 hours 62.638 hours 47.918 hours 19. A certain car depreciates in value at a continuous rate of 1.9%. How many years does it take for the car's value to depreciate to # of its original value? O 13.157 years O 39.471 years O 15.141 years O 72.962 years 4.938 years12. For the function f, fi(a) = -2x +1 and f (-2) = -4. Find the approximation for f (-1.6) by using the line tangent to the graph of f at a = -2. O -5 O -2 O -6.56 O -12 O -2.16 13. Evaluate foldx. O OF + + C O +C Of+#+C 14. f(- sin x cos' ) da = O O O sin " cus' a + 0 O cus 1+ C C 15. Calculate the following limit: O -1/3 2/3 O -6 O -49. Which differential equation describes the slope field shown below? - NWA G L -4 0 2 3 04=ex-1 O= = Vy+1 0 4 =2x+7 =y+1 0 = (2-4)2-1 10. Using the line tangent to the curve f (x) - In(x) + 1 at a = e, what is the local linear approximation for f (3)? Notice that e = 2.718 is close to 3, so this approximation will be fairly accurate. 6-20+ 2 Oe-2 01-1 O:+2 O 2+1 11. Using the line tangent to the curve f (2) = x - 2 atx =1, what is the local linear approximation for f (1.3)? -0.31 1.6 O -0.4 O -0.6 0.226. The slope field for a specific differential equation is shown below. w O - N N -3 -3 -2 0 2 3 Which of the following could be a solution to the differential equation with an initial condition of y(1) = 1? Oy=1-2 Ov= 2+1 Oy= 2 In(x) Oy=2v2x -1-1 Oy=1-2v2x -1-1 7. The slope field for a specific differential equation is shown below. w N - L O -2 -3 -4 -3 -2 -1 0 2 3 Which of the following could be a solution to the differential equation with an initial condition of y(0) = 2? Oy=1-ed Ou=e*+1 Oy= In(x) +1 Ov= =+1 Oy=1-In()20. (% error) = (actual value] [approximated value) (actual value) X 100% Use the formula above to find the answer to the following question: If the local linear approximation of f (2) = =152 at x-2 is used to find the approximation for f (2.2), then the % error of this approximation is... less than 2%. O between 2% and 5%. O between 5% and 8%. O between 8% and 11%. O between 11% and 14%. 21. Given that [), / (-4) de = -5, which of the following must be true? O 512 f (p) dp = -25 O -$ 5: f (p) dp = 1 O -5 /2 f(p) dp = -5 0 5 / jf (p) dp = -5 O -1 5 f (p) dp = -25