Advanced Math Section 4.2 Exponential Growth Name

Advanced Math Section 4.2 Exponential Growth Name: [Day 1] April 2015

Define: Exponential Function:

Exponential Growth:

Example 1: Without a calculator, evaluate the exponential function. a. when and when b.

Example 2: With a calculator, evaluate the exponential function. a. when and when b. when and when

c. when and when d. when and when

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

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

FOR ALL APPLICATION PROBLEMS, SHOW IN THE GIVEN FORMULA HOW YOU ARE PLUGGING IN THE NUMBERS, THEN YOU CAN USE YOUR CALCULATOR!

Example 4: The monthly income, , in dollars from a new product is given by the following equation:

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?

b. What is the monthly income after two years?

c. What is the monthly income after the 100th month? Example 5: The population, , of a city grows exponentially according to the following function:

where is the time, in years. a. To the nearest hundred, find the population of the city after 3 years.

b. To the nearest hundred, find the population of the city after 4.25 years.

c. What do you think will happen if the time, , continues to increasing?

d. Is your answer in part c feasible?

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 No additional money was deposited or withdrawn from this account.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:

a. How much money was in the account when Charlie started high school (assume ?

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:

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?

b. How much more money will she have at the end of four years than her starting deposit?

c. Do you think this is enough to purchase a car?

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?

e. If Diane doesn’t make any deposits or withdrawals from the account, how much money will she have at the end of years?

f. How does the answer to part e compare to Diane’s initial investment?

HW: (1) Finish Note Sheet (2) Page 354-355 #1, 3, 9, 11, 13, 17, 19, 49a (3) Page 400 #1