Algebra 2 Name: __________________ Date/Hr: __________________ Exponential Growth and Decay Applications Growth/Decay Models Compound Interest 𝑡 𝑟 𝑛𝑡 𝑦 = 𝑎(1 ± 𝑟) 𝐴 = 𝑃 (1 + ) 𝑛 y: amount of quantity after t years A: amount in account after t years a: initial amount P: initial principal r: percentage increase or decrease r: annual rate t: time in years n: number of time compounded per year (1±r): growth/decay factor Write an exponential growth or decay model that describes the situation. 1. In 1992, 1219 monk parakeets were observed in the United States. For the next 11 years, about 12% more parakeets were observed each year. 2. You deposit $800 in an account that pays 2% annual interest compounded daily. 3. A new car costs $25,000. The value of the car decreases 15% each year. Problem Solving. 4. In 1990, the population of Austin, Texas, was 494,290. During the next 10 years, the population increased by about 3% each year. a. Write a model giving the population P of Austin t years after 1990. What was the population in 2000? b. Graph the model and state the domain and range. c. Estimate the year when the population was about 590,000. 5. You deposit $2200 in a bank account. Find the balance after 4 years for each of the situations described below. a. The account pays 2.25% annual interest compounded quarterly. b. The account pays 3.5% annual interest compounded monthly. c. The account pays 4% annual interest compounded yearly. 6. When a plant or animal dies, it stops acquiring carbon-14 from the atmosphere. Carbon-14 decays over time with a half-life of about 5730 years. The percent P of the original amount of carbon-14 that remains in a sample after t years given the equation: 𝑡 1 5730 𝑃 = 100 ( ) 2 a. What percent of the original cabon-14 remains in a sample after 2500 years? 5000 years? 10,000 years? b. Graph the model. c. An archaeologist found a bison bone that contained about 37% carbon-14 present when the bison died. Use the graph to estimate the age of the bone when it was found. 7. The yearly cost for residents to attend a state university has increased from $5200 to $9000 in the last 5 years. a. To the nearest tenth of a percent, what has been the average annual growth rate in cost? b. If this growth rate continues, what will the cost be in 5 more years?