1 / 10

MTH-5107 Pretest A Modified

MTH-5107 Pretest A Modified. 1. A city whose population was 28000 at the beginning of the century saw its population multiply by 1.1 every 4 years. What exponential expression represents the number of inhabitants (h) of this city as a function of the number of years (t) that have passed?.

olwen
Download Presentation

MTH-5107 Pretest A Modified

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MTH-5107 Pretest A Modified 1. A city whose population was 28000 at the beginning of the century saw its population multiply by 1.1 every 4 years. What exponential expression represents the number of inhabitants (h) of this city as a function of the number of years (t) that have passed? Starting population = a = 28000 c = 1.1 2. Use algebra to solve the following equation. Show all steps in your solution, 2 x – 3 • 8 x + 1 = 32 x - 2 2 x – 3 • (23) x + 1 = (25) x – 2 2 x – 3 • 2 3x + 3 = 25x – 10 2 (x – 3) + (3x + 3) = 25x – 10 24x = 25x – 10 24x = 25x – 10 4x = 5x – 10 -x = -10 x = 10 3. Use algebra to solve the following equation. Show all steps in your solution, 7.5 x + 2 = 3 5x - 1 log 7.5 x + 2 = log 3 5x – 1 (x + 2) log 7.5 = (5x – 1) log 3 x log 7.5 + 2 log 7.5 = 5x log 3 – log 3 x log 7.5 - 5x log 3 = – log 3 - 2 log 7.5 x(log 7.5 – 5 log 3) = – log 3 - 2 log 7.5

  2. 4. Find the inverse of the function: f(x) = -3x + 2 y = -3x + 2 3x = -y + 2 Inverse: 3y = -x + 2 y = log3 (-x + 2) f-1(x) = log3 (-x + 2) 5. Given the graph below and the expression of the function, determine the statement below that describes the parameters. f(x) = logc (b(x – h)) • b > 0; 0 < c < 1 and h = 0 • b = 0; c > 1 and h > 0 • b > 0; c > 1 and h < 0 • b > 0; c > 1 and h = 0 • b < 0; 0 < c < 1 and h > 0 • b > 0; 0 < c < 1 and h = 0 • b = 0; c > 1 and h > 0 • b > 0; c > 1 and h < 0 • b > 0; c > 1 and h = 0 • b < 0; 0 < c < 1 and h > 0 Function falls to the right of the asymptote  b > 0 Equation of the asymptote is x = 0  h = 0 ab > 0 and function is increasing  c > 1

  3. 6. Given the graphs below and the expressions of the functions, determine the statement below that describes the parameters of g(x). f(x) = cx g(x) = a•cx + k • a > 0; 0 < c < 1 and k < 0 • 0 < a < 1; c > 1 and k < 0 • a > 1; c > 1 and k < 0 • 0 < a < 1; c > 1 and k > 0 • a > 1; c > 1 and k > 0 Function falls above the asymptote  a > 0 Equation of the asymptote is y = -2  k < 0 ab > 0 and function is increasing  c > 1 Function g turns more sharply away from asymptote that function f  a > 1

  4. The zero is positive. • The y-intercept is 0.75. • It is increasing and c > 1. • It is negative in the interval • Its asymptote is x = 0. 7. Each of the statements below apply to one of the two following functions. State which function applies to each. f(x) g(x) f(x) f(x) f(x) Function f: ab > 0 and c > 1 f is increasing

  5. 8. Consider the function below and determine whether the following statements are true or false. If false make them true. True • The zero is positive. • Its domain is x > 1. • Its asymptote is x = 6. • Its range is R. • The y-intercept is 6. True False True False x = h x = 1 Its asymptote is x = 1 2(x – 1) > 0 2x – 2 > 0 2x > 2 x > 1

  6. 9. An exponential function passes through the point(-2, 15) and its asymptote is y = -10. Determine the rule of correspondence for this function. y = cx – 10 15 = c-2 – 10 c-2 = 15 + 10 c-2 = 25 c = 5 f(x) = ±cx + k f(x) = cx - 10 k = -10 y1 > k,  a is + f(x) = 5x - 10 • You invest $1500 into an annual-interest account, compounded semi-annually. • a) What rule of correspondence determines the balance B(t) as a function of the number of years (t) invested? • b) At what interest rate would this sum double in 6 years? B(t) = 1500•c2t Interest Rate = 1.0595 – 1 = 0.0595 = 5.95% … over half a year 5.95% × 2 = 11.9%

  7. In a lake where fishing is not permitted, 250 lake trout are stocked.. We determine that the population (y) of the trout living in the lake corresponds to the equation below. • a) After 1 year the number of trout is determined to be 300. Determine the value of k. • b) How many years must pass before permitting fishing if a population of 1500 trout are required? Round your answer to the nearest year. k is a constant t is number of years since the lake was stocked y = 250ekt y = 250e0.182t 10 years must pass before fishing is allowed.

  8. 12. Determine the value of the following expression given that . 13. Reduce the following logarithmic expression to its simplest form.

  9. 14. Circle the letter which corresponds to equivalent of the following expression: 15. Solve for x: b) log3 (2x + 1) + log3 (x – 3) = 2 a) ln(2x + 1) – ln(x – 2) = ln10 Restr#1 2x + 1 > 0 2x > -1 x > -0.5 Restr#1 2x + 1 > 0 2x > -1 x > -0.5 Restr#2 x - 2 > 0 x > 2 Restr#2 x - 3 > 0 x > 3

  10. 16. Given the following statements, circle the ones that are false and restate them to make them true. True False False True True

More Related