- The Power of Exponential Growth and Decay Learning Targets: I can recognize situations in which a quantity grows or decays by a constant percent rate. I can write an exponential function to model a real life situation that involves growth or decay by a constant percent rate. Opening Activity Malik bought a new car for $15,000. As he drove it off the lot, his best friend, Will, told him that the car s value just dropped by 15% and that it would continue to depreciate 15% of its current value each year. If the car s value is now $12, 750 (according to Will), what will its value be after 5 years? a. Complete the table below Number of years, t, passed since driving the car off the lot Car value after t years 0 $12,750.00 1 2 3 4 5 b. Write a formula for the sequence that models the value of Malik s car t years after driving it off the lot. Exponential Formula c. Use the formula from part (b) to determine the value of Malik s car 7 years after its purchase. Round your answer to the nearest cent. d. Identify the growth or decay factor e. Create a sketch to represent the graph of this function
- The Power of Exponential Growth and Decay Review Problem Set 1. Mr. Smith invested $2,500 in a savings account that earns 3% interest compounded annually. He made no additional deposits or withdrawals. Which expression can be used to determine the number of dollars in this account at the end of 4 years? ( 2500(1.0 4 ( 2500(0.97) 4 ( 2500(1.0 3 ( 2500(0.96) 3 Exponential formula 2. Jessica invested $6000 in an account at a 4% interest rate compounded annually. She made no deposits or withdrawals on the account for 4 years. Exponential formula Determine to the nearest dollar, the balance in the account after the 4 years. Determine to the nearest cents, the balance in the account after the 4 years. 3. Some banks charge a fee on savings accounts that are left inactive for an extended period of time. The equation represents the value, y, of one account that was left inactive for a period of x years. What is the y-intercept of this equation and what does it represent? 0.98, the percent of money in the account initially 0.98, the percent of money in the account after x years 5000, the amount of money in the account initially 5000, the amount of money in the account after x years 4. The value in dollars,, of a certain car after x years is represented by the equation years? 2589 6510 15,901 18,490. To the nearest dollar, how much more is the car worth after 2 years than after 3
5. Krystal was given $3000 when she turned 2 years old. Her parents invested it at a 2% interest rate compounded annually. No deposits or withdrawals were made. Which expression can be used to determine how much money Krystal had in the account when she turned 18? 6. Miriam and Jessica are growing bacteria in a laboratory. Miriam uses the growth function while Jessica uses the function, where n represents the initial number of bacteria and t is the time, in hours. If Miriam starts with 16 bacteria, how many bacteria should Jessica start with to achieve the same growth over time? 32 16 8 4 7. The breakdown of a sample of a chemical compound is represented by the function, where represents the number of milligrams of the substance and t represents the time, in years. In the function, explain what 0.5 and 300 represent. 0.5 is the and 300 is the. 8. The table at right represents the function F. The equation that represents this function is
- The Power of Exponential Growth and Decay Homework 1. Scientists are studying how quickly the population of an invasive species of beetle will increase in a controlled farm setting. They calculate that the population is increasing at a steady rate of 6% per week. At the beginning of the week, the population was 350 beetles. (a) Write a formula to model the growth of the population of beetles Growth or Decay Factor Initial value (y-intercept) Exponential Formula (b) Find the population of beetles a week later (c) Sketch the graph that model the growth of population of beetles 2. A cup of coffee is cooling down such that its temperature is decreasing at a steady rate of 8% per minute. Let s say the coffee starts at a temperature of 200F. a. Write a formula to model the temperature of water after m minutes Growth or Decay Factor Initial value (y-intercept) Exponential Formula b. Find its temperature after one minute. c. What will be the temperature after four minutes? d. Sketch the graph that model the cooling down process
3. A construction company purchased some equipment costing $300,000. The value of the equipment depreciates (decreases) at a rate of 14% per year. a. Write a formula that models the value of the equipment. b. What is the value of the equipment after 9 years? c. Sketch the graph that model the cooling down process d. Estimate when the equipment will have a value of $50,000. 4. A car depreciates (loses value) at a rate of 4.5% annually. Greg purchased a car for $12,500. Which equation can be used to determine the value of the car, V, after 5 years? 5. Pablo invested $9,000 in an account at a 6% interest rate compounded annually. She made no deposits or withdrawals on the account for 5 years. Growth or decay factor Initial value/y-intercept Exponential formula Determine to the nearest dollar, the balance in the account after the 5 years. Determine to the nearest cent, the balance in the account after the 5 years.