original answer please. No plagiarism.
1. Useful concepts
How do you think you will use the information you learned in this course in the future? Which concepts will be most important to you? Explain why. Which do you anticipate will be the least important? Explain why.
2.Exponents and Logs
What is the relationship between exponents and logarithms? How is an exponential function related to a logarithmic function graphically? What is the difference between log(x) and ln(x)? What is the ratio log(x)/ln(x)?
3.Follow the bouncing ball
A golf ball is dropped from 10 m. On each bounce, it bounces back up half as far as it last fell. What is the total distance the ball travels through its first four bounces? Through the first eight? The first two million?
Once upon a time, a grade school teacher needed to step out of the classroom, so to occupy his young students for a few minutes he asked them to sum the integers from 1 to 400. However, before he could get out the door, one student raised her hand and said, “The answer is eighty thousand, two hundred.” Astonished, the teacher asked how she arrived at this answer so quickly. How did the child do this?
After graduating from UoP you immediately get many excellent job offers. The manager at one company is rather eccentric, and offers you an unusual pay scale. You will earn one penny on the first day, two cents for day two, etc., with each day’s salary being double the previous day, up to the 30th day, at which point it will remain fixed at that level. How much will you make total in the first 15 days? Will you accept this job offer? Why or why not? Explain all your reasoning in detail.