Logarithms and Exponential Functions.

Identify the choice that best completes the statement or answers the question.

  1. Solve for x.
  1. 3 b. 9 c. 20.25 d. 324
  1. Evaluate .
  1. n b. c. mn d. 2n
  1. The function relates the speed of the wind near the centre of a tornado in miles per hour, to d, the distance that the tornado travels, in miles. If winds near the center of the tornado reach speeds of 400 mph, estimate the distance it can travel.
  1. 130 miles b. 13000 miles c. 13 miles d. 1.1666 miles
  1. Evaluate .
  1. 4 b. 5 c. 7 d. 10
  1. Evaluate
  1. 2 b. 3 c. 8 d. 16
  1. Solve for x.
  1. b. -1 c. 5 d.
  1. Solve
  1. b. 8 c. 300 d.
  1. Solve .
  1. -5, 2 b. 10 c. 2 d. 7
  1. Write the logarithmic expression as a single logarithm:
  1. Expand the logarithmic expression:
  1. Use the properties of logarithms to evaluate
  2. 7b. 11c. 9d. 5
  1. Use a graphing calculator to solve by graphing. Round to the nearest hundredth.
  2. 5.22b. 2.61c. 2.40d. 26.43
  1. Use the Change of Base Formula to solve Round to the nearest hundredth.
  2. 19.0298b. 1.1894c. 4.7574d. 12.9837
  1. Graph

  1. Which of the following represents a shift of 5 units right and 6 units up from the graph of ?
  1. Solve
  2. 30b.c. 110d. -3.23
  1. The amount of money in an account with continuously compounded interest is given by the formula , where P is the principal, r is the annual interest rate, and t is the time in years. Calculate to the nearest tenth of a year how long it takes for an amount of money to double if interest is compounded continuously at 3.1%. Round to the nearest tenth.
  2. 2.2 yrb. 13.8 yrc. 22.4 yrd. 15.5 yr
  1. Solve . Round to the nearest ten- thousandth.
  2. 0.4036b. 0.2727c. 1.0909d. 1.9091
  1. How much money invested at 3% compounded monthly for 3 years will yield $520?
  2. $148.78b. $179.42c. $358.84d. $475.30
  1. What is the inverse of the function: ?
  1. Suppose you invest $1200 at an annual interest rate of 2.3% compounded continuously. How much will you have in the account after 4 years?
  2. $1,211.08b. $1,315.64c. $2,746.64d. $3,574.47
  1. The half-life of a certain radioactive material is 85 days. An initial amount of the material has a mass of 801 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 10 days. Round your answer to the nearest thousandth.
  1. What is the inverse of the function ?
  1. Write an exponential function for a graph that includes (1, 12) and (0, 9).
  1. Solve the equation
  2. 96b. 81c. 26.8d. 6.45
  1. If there are initially 2200 bacteria in a culture, and the number of bacteria triple each hour, the number of bacteria after t hours can be found using the formula How long will it take the culture to grow to 60,000 bacteria?
  2. 5.06 hrb. 4.25 hrc. 3.01 hrd. 1.52 hr
  1. What is
  2. Which is equivalent to ?
  1. What is the value of ?
  2. 1b. 2c. 5d. 6
  1. Solve for x:
  2. -3b. c. 3d. 13
  1. Solve for x:
  2. b. 5c. 12d. 18
  1. Solve:
  2. 9b. 24c. 26d. 31
  1. Solve:
  2. 4b. 8c. 14d. 32
  1. Given , which best approximates x ?
  2. 0.35b. 1.17c. 1.58d. 2.25
  1. Solve:
  2. 0.176b. 0.631c. 1.500d. 1.585
  1. Solve:
  1. What is the domain of y=
  1. What is the range of
  1. Which is the inverse of
  1. Which graph represents the inverse of the function shown?