<p>Advanced Math Section 4.2 Exponential Growth Name: [Day 1] April 2015</p><p>Define: Exponential Function:</p><p>Exponential Growth:</p><p>Example 1: Without a calculator, evaluate the exponential function. a. when and when b.</p><p>Example 2: With a calculator, evaluate the exponential function. a. when and when b. when and when </p><p> c. when and when d. when and when </p><p>Example 3: (1) Sketch the graph of the exponential function using the following domain for : (2) Describe how you can tell by looking at the graph that it is an example of exponential growth</p><p> a. b. Example 3: (1) Sketch the graph of the exponential function using the following domain for : (2) Describe how you can tell by looking at the graph that it is an example of exponential growth</p><p> c. d. </p><p>FOR ALL APPLICATION PROBLEMS, SHOW IN THE GIVEN FORMULA HOW YOU ARE PLUGGING IN THE NUMBERS, THEN YOU CAN USE YOUR CALCULATOR!</p><p>Example 4: The monthly income, , in dollars from a new product is given by the following equation:</p><p> where is the time, in months, since the product was first put on the market. a. What is the monthly income after the 10th month?</p><p> b. What is the monthly income after two years?</p><p> c. What is the monthly income after the 100th month? Example 5: The population, , of a city grows exponentially according to the following function:</p><p> where is the time, in years. a. To the nearest hundred, find the population of the city after 3 years.</p><p> b. To the nearest hundred, find the population of the city after 4.25 years.</p><p> c. What do you think will happen if the time, , continues to increasing?</p><p> d. Is your answer in part c feasible?</p><p>Example 6: When Charlie was born, his parents opened an account to help save money for when Charlie would attend college. They deposited $25000 and let the money sit in the account and earn interest. No additional money was deposited or withdrawn from this account. The amount of money in the account, , after years, is given by the following equation:</p><p> a. How much money was in the account when Charlie started high school (assume ?</p><p> b. How much money was in the account when Charlie finished high school (assume ? Example 7: Diane is saving money to purchase a car after college. For her graduation, she received monetary gifts totaling $3750. She invests her money in an account that earns interest continuously. The amount of money in the account, , after years, is given by the following equation:</p><p> a. If Diane doesn’t make any deposits or withdrawals from the account, how much money will she have at the end of four years?</p><p> b. How much more money will she have at the end of four years than her starting deposit?</p><p> c. Do you think this is enough to purchase a car?</p><p> d. If Diane doesn’t make any deposits or withdrawals from the account, how much money will she have at the end of eight years?</p><p> e. If Diane doesn’t make any deposits or withdrawals from the account, how much money will she have at the end of years?</p><p> f. How does the answer to part e compare to Diane’s initial investment?</p><p>HW: (1) Finish Note Sheet (2) Page 354-355 #1, 3, 9, 11, 13, 17, 19, 49a (3) Page 400 #1</p>