Math 1320 - Lab 4
Name:
Today we will consider a set of questions concerning sequences and series. Answer the questions
below and be sure explain your reasoning behind your approach to these questions with appropriate diagrams and complete sentences. In your writing, try to be complete enough so that
someone who has completed Math 1310 would understand what you are doing and why you are
doing it. Remember, the goal of the lab session is to make sure you know how to approach each
of these problems. If you can finish the math part over the weekend you can work with Dr.
Skorczewski or Olakunle to get the writing done well.
1.
(10 points) Fish farming: A fish farmer has 5000 catfish in his pond. The number of
catfish increases by 8% per month and the farmer harvests 300 catfish each month. Find a
recursive relationship that shows the catfish population Pn after n months. What is P0 ? How
many catfish are in the pond after 6 months?
2.
(10 points) Sustainability versus growth: Suppose a first-grader running a lemonade
stand makes a 1-dollar profit on day one (i = 1) and then takes half of the profit to re-invest to
prepare for the next day. On day two she makes half a dollar and re-invests 1/3-dollars, and so
on for subsequent days on to infiinity. Compose the sum of the net daily balance over all days
and determine its total value.
3.
(10 points) Bouncing ball: Suppose a ball is dropped from 2 meters height and bounces
to 1.5 meters on the second bounce, and 9/8ths of a meter on the second bounce, and so on
indefinitely. What is the total vertical distance traveled by the ball?