Unit 8 TEST REVIEW: Modeling with Exponential & Logarithmic Functions

  1. If a credit card company charges 16% yearly interest, which of the following calculations would be used in the process of calculating the monthly interest rate?

a. b. c. d.

  1. A population of 35 rabbits is increasing by a rate of 8.5% per day. Which of the following is the closest to the number of days it will take for the rabbit population to double?

a. 1b. 8c. 5d. 82

  1. An equation to represent the value of a fundq quartersafter the car was bought can be modeled by the function. Which statement(s)is/are not correct?
  1. The cost of the car is decreasing at a rate of approximately 15% per quarter.
  2. The cost of the car is decreasing at a rate of approximately 4% per quarter.
  3. The cost of the car is decreasing at a rate of approximately 15% per year.
  4. The cost of the car is decreasing at a rate of approximately 85% per year.
  1. II and IIIb. I and IVc. I, II and IIId. II, III, and IV
  1. 480 grams of a substance is decaying at a rate of 2.8% per year compounded continuously. How much of the substance remains after 10 years, to the nearest gram?
  1. A population is decaying at a rate of 14.6% every 3 years.

a. What is the percent rate of decay per year? Round your final answer to the nearest hundredth of a percent.

b. What is the percent rate of decay over 5 years? Round your final answer to the nearest hundredth of a percent.

  1. Find the solution to each of the following exponential equations. Express your final answers to the nearest hundredth.

a. 53x = 246b. c. = 87

  1. An investment of $600 is made at 3.4% yearly interest, compounded weekly.

a. Write an equation that models the amount A the investment is worth t-years after the principal is invested.

b. How much is the investment worth after 15 years, to the nearest cent.

c. Algebraically determine the number of years it will take for the investment to double, to the nearest tenth of a year.

  1. Plutonium has a half-life of 87.7 years. A scientist starts with a sample of 600 kilograms of plutonium.

a. Write a function, H(t), to model the amount of Plutonium left after t years.

b. WriteH(t)in the form, . Round to the nearest thousandth.

c. By what percent is plutonium decaying each year, to the nearesttenth of a percent?

  1. The population of a small country is decreasing .575% per year. Originally there were 567,800 people in the country. Write an equation to model the number of people left in the country after t-years.
  1. The height in feet of a young cherry tree planted in Washington, D.C. can be modeled by the function,

, where x is the number of years after the tree was planted.

  1. What is the y-intercept of f(x)? Interpret this value in the context of the problem.
  1. Interpret f(5)=17.04 in the context of the problem.
  1. Find the average rate of change of the function for the following intervals: and , to the nearest tenth. Explain what each rate of change means in the context of the problem, and state one conclusion you can make about the growth of the Higan tree based on your answers.
  1. A deposit of $2,500 is made into a bank account that gets 43% interest, compounded quarterly.
  2. Write a function, A(t), to model the amount of money in the account after t-years.
  1. Write A(t) in the form .
  1. By what percent is the account growing each year?
  1. A population of rabbits t years after the population was 10 rabbits can be modeled by the function, . Write an equivalent function for the number of rabbitsm months after the population was 10 rabbits. Round to the nearest thousandth.
  1. The formula , models the temperature of a warming or cooling substance t minutes after the substance has been placed in new surroundings where is the temperature of the surroundings, is the initial temperature of the substance, k is the percent rate, expressed as a decimal, that the substance changes temperature, each minute (note: in this formula, k is always positive).
  2. A hot liquid starts at a temperature of 188°F and cools down in a room that is held at a constant temperature of 68°F. The temperature of the liquid changes at a rate of 4.03% per minute. Write a function, C(t),to represent the temperature of the liquid t minutes after it began cooling.
  1. At the same time, as the hot liquid began cooling, a frozen meal is taken out of the freezerkept at a temperature of and placed in an oven preheated to a temperature of . The temperature of the meal changes at a rate of 2.43% per minute. Write a function, W(t), to model the temperature of the mealt minutes after it was placed in the oven.

  1. Graph C(t) and W(t) where .
  1. Graphically determine how many minutes, to the nearest tenth,it will take for the temperature of the liquid be the same as the temperature of the meal?