Which Would You Choose? You have just been offered a job that will last one month. You have two salary options. You can either receive a salary of one million dollars for the month’s work, or you can receive one penny for your first day on the job, and then double the previous day’s pay for each of the remaining 30 days. Which salary option would you choose?

Day 1: $.01 Day 2: $.02 Day 3: $.04 Day 4: $.08 Day 5: $.16 Day 6: $.32 Day 7: $.64 Day 8: $1.28 Day 9: $2.56 Day 10: $5.12 Day 11: $10.24 Day 12: $20.48 Day 13: $40.96 Day 14: $81.92 Day 15: $ Day 16: $ Day 17: $ Day 18: $1, Day 19: $2, Day 20: $5, Day 21: $10, Day 22: $20, Day 23: $41, Day 24: $83, Day 25: $167, Day 26: $335, Day 27: $671, Day 28: $1,342, Day 29: $2,684, Day 30: $5,368, Total Salary for 30 days: $10,737,418.23

How do we get this …

Brown Marmorated Stink BugBrown Marmorated Stink Bug (Video) …from this?

Brown Marmorated Stink Bug Introduced to US in 1996

Brown Marmorated Stink Bug Distribution, June 2015

Brown marmorated stink bugs tend to live only one year here in the United States. A female brown marmorated stink bug can lay up to 400 eggs per year. Estimate the population growth after two generations. Generation 1: 400 stink bugsMales: 200Females: 200 Generation 2: 200 females lay 400 eggs each= 200 females x 400 eggs/female = 80,000 eggs  80,000 stink bugs

A caretaker is responsible for a pond with water lilies floating on its surface. The lily population doubles in size every day. If left unchecked, the water lilies will smother the pond in 30 days, killing all the other living things in the water. Day after day, there seem to be very few plants on the surface of the pond, so the caretaker decides to leave the water lilies to grow until they half- cover the pond before cutting them back. On what day will the caretaker need to cut back the water lilies?

Exponential Growth: Populations growing by a fixed percent experience exponential growth. Every incremental increase in number is larger than the one before it. Exponential growth in nature occurs only when populations have plenty of food and space and have no competition or predators, usually when organisms are introduced to a new environment. J-curve represents exponential growth

The graph below shows the population of some reindeer that were introduced to an Alaskan island in (1)Describe the population’s changes over time (2)During what years did the population experience exponential growth? (3)What might have happened in 1937?