Concept explainers
Work these exercises. (see Example 11.)
Finance An amount of $12,000 is deposited in an account with an interest rate of r percent per year, compounded monthly. At the end of 8 years, the balance in the account is given by
a. Find
b. Find
Want to see the full answer?
Check out a sample textbook solutionChapter 11 Solutions
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
- Graphical Reasoning Graph the exponential function y=ax for a=0.5,1.2 and 2.0. Which of these curves intersects the line y=x ? Determine all positive numbers a for which the curve y=ax intersects the line y=x.arrow_forwardTerry is skiing down a steep hill. Terry’s elevation, E(t),in feet after tseconds is given by E(t)=300070t. Write a complete sentence describing Terry’s startingelevation and how it is changing over time.arrow_forwardJohn opens a savings account and decides to deposit $10 each month. Let x represent the number of months that he has been saving, and y represent the total amount of money saved. 1. What is the algebraic equation for John's saving plan?2. How much money will John have saved in 14 months? In 6 months? Show your work and explain.3. In how many months will John have saved $100? $175? Show your work and explain.4. What is the rate of change?5. How does knowing the rate of change help you in answering questions in this problem? 6. Use your equation to complete the table representing John's savings: # of Months Saving Account Balance ($)01234arrow_forward
- ANSWER ALL THE QU A 200g sample of radioactive polonium-210 has a half-life of 138 days. This means that every 138 days, the amount of polonium left in the sample is half of the original amount. a) Write an equation that models the amount of Polonium b) What mass of Polonium-210 is left after 2 years? c) Determine how long it will take for the sample to reduce to 150g The University of McMaster undergraduate program is growing at a rate of 3% each year. The current enrollment is 12400. Determine when the enrollment will reach 13250. You have found an investment at the bank that pays 2.4% interest per year for 10 years. How much should you invest now so that you have $2000 at the end of the 10 years?arrow_forwardNot use excel Suppose that you have an investment that earns 0% in the first year, but 20.7% in the second year. What rate of interest, compounded annually, would yield the same return after two years? (Answer in percentage)arrow_forwardA stock account started with a value of $95,000 in the year 1995. The value of the account appreciated to $160,000 by the year 2002. i) What was the annual growth rate between 1995 and 2002? Write your answer as a decimal rounded to 4 decimal places. Show all work. Write your answer in a complete sentence form. ii) Assume that the stock value continues to grow by the same percentage. What will the value equal in the year 2005 ? Show all work and any equations you use. Round to the nearest thousand dollars. Write your answer in a complete sentence form.arrow_forward
- A bacteria culture grows with constant relative growth rate. The bacteria count was 400 after 2 hours and 25, 600 after 6 hours.(a) What is the relative growth rate? Express your answer as a percentage.(b) What was the initial size of the culture?(c) Find an expression for the number of bacteria after thours.(d) Find the number of cells after 4.5 hours.(e) Find the rate of growth after 4.5 hours.(f) When will the population reach 50,000?arrow_forwardYour car's resale value depreciates according to the following table. x is years since purchase and y is the resale value. x y 0 42,000 1 35,280 2 29,635 3 24,894 4 20,911 5 17,565 a) write an equation to model this situation b) what is the decay rate? (how much does the price of the car depreciate each year?) c) In what year will the car be worth 20% of itws initial value? Show your solution mathematically and on a graph.arrow_forwardGive your answer as a percentage, accurate to three decimal places.Your account value grows by 4% this year. What percentage gain do you need next year in order to: have a total of 10% growth? % average 10% growth per year? %What percentage loss can you take next year and still break even?arrow_forward
- The table represents an exponential function with a horizontal asymptote at y = –1. x -3 -2 -1 0 1 2 3 y 80 26 8 2 0 -2/3 -8/9 Create a graph of the function and use it to answer the questions.Part A: What is the end behavior of the function? Explain your reasoning. Part B: What are the positive and negative intervals? Explain your reasoning.Part C: What is the percent rate of change? Show all necessary calculations. Part D: What are the domain and range?arrow_forwardDetermind the time necessary for P dollars to double when it is invested at an interest rate r compounded anually, monthly, daily, and continuously. R=7.1%arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning