* 1. * 2.

* Review the P.O.T.D. * Review compounding continuously * Exponential and e word problems

* 1. * x = -1

* 2. * x = 1, x = -6

* A is the balance in the account after t years. * P is the principal amount put into the account. * n is the number of compounds per year. * r is the rate at which the interest is compounded (always in decimal form).

* A total of $12,000 is invested at an annual interest rate of 9%. Find the balance after 5 years if it is compounded: * Quarterly

*P*P * Principal amount we are investing * $12,000 *r*r * annual interest rate * 9% *n*n * How many compounds per year *4*4 *t*t * How long we are investing (in years) * 5 years

* We solve for A. * A = $18,788.17

How often is it compounded?Computation Annually or Yearly Twice a year Quarterly Monthly Weekly Daily Hourly Every Minute Every Second

* e ≈ … * A = Pe rt

* A total of $7,500 is invested at an annual interest rate of 4%. Find the balance after 10 years if it is compounded continuously. * A :What we’re trying to find * P: * * e: * is our natural base * e ≈2.71 * r: * 0.04 * t: * 10

* A = $11,188.69

* Scientists are able to use the idea of exponential decay to determine how much of a specific element is left over after a specific amount of time elapses. * * For instance, in 1986, a nuclear reactor melted down in Chernobyl (Soviet Union at the time). The meltdown spread highly toxic radioactive chemicals, such as plutonium, over hundreds of square miles, and the government evacuated the city and surrounding areas. To see why the city is now uninhabited, consider the model:

* Where P is the amount of plutonium that remains (from the initial amount of 10 pounds) after t years. Note that from this model, the half-life of the plutonium is about 24,100 years. That is after 24,100 years half of the original amount will remain. Wow! That’s a long time! * * Go ahead and graph this function on the plane below. Be sure to label the axes according to the function and use the appropriate scale.

* The population P (in millions) of Russia from 1996 to 2004 can be approximated by the model: * * P = e t. * * Where t represents the year, with t = 6 corresponding to 1996.

* A. * Using the model, anticipate what will happen with Russia’s population in the future.

* B. * According to the model, is the population of Russia increasing or decreasing? Explain.

* C. * Find the population of Russia in 1998 and 2000.

* D. * Use the model to predict the population of Russia in 2020.

* Let Q represent a mass of radioactive radium ( 226 Ra) (in grams), whose half-life is 1599 years. The quantity of radium present after t years is

* A. * Determine the initial quantity (when t = 0).

* B. * Determine the quantity present after 1000 years.

* C. * Use a graphing utility to graph the function over the interval t = 0 to t = 5000.

* What questions do we have?

* Page: 227 * Numbers: 63, 68 * Due: January 19,2016