Exponential Growth and Decay: Population Growth and Compound Interest, Study notes of Algebra

Download Exponential Growth and Decay: Population Growth and Compound Interest and more Study notes Algebra in PDF only on Docsity! Math 140 E2 Nov.10,2008 4.6 Applications and Models: Growth and Decay; Compound Interest 1. Population Growth: P (t) = P0ekt where k is called exponential growth rate, P0 is the population at time 0, P is the population after time t Example1 In 2005, the population of China was about 1.306 billion, and the exponential growth rate was 0.6% per year (1)Find the exponential growth function (2)Estimate the population in 2008 (3)After how long will the population be double what it was in 2005? 2. Interest Compound Continuously : An amount P0 is invested in a savings account at in- terest rate k compound continuously. The amount P (t) in the account after t years is given by P (t) = P0ekt Example 2: In 1626, Peter Minuit of the Dutch West India Company purchased Man- hattan Island from Native Americans for $24. Assuming an exponential rate of inflation of 6% per year, how much will Manhattan be worth in 2010? Example 3: On Jan 2,2004, $2000 is placed in an Individual Retirement Account(IRA) that will pay interest of 10% per annum compounded continuously (1)What is the interest rate? (2)What will IRA be worth on Jan 1, 2024? (3)After how long will the $2000 have doubled? 3. Growth rant and doubling time: kT = ln 2, or k = ln 2 T , or T = ln 2 k 4. Exponential Decay: The amount P of a radioactive material present at time t is given by P (t) = P0e−kt, k > 0 where P0 is the original amount of radioactive material and k is a positive number that represents the rate of decay. All radioactive substances have a specific half-life, which is the time required foa half of the radioactive substance to decay. Example 4: Traces of burned wood along with ancient stone tools in an archeological dig in Chile were found to contain approximately 1.67% of the original amount of carbon 14. If the half-life of carbon 14 is 5600 years, approximately when was the tree cut and burned? 1