# Analysis of Bacterial Growth in the Hall of Science In the Hall of Science, a biology major is tracking the growth of a certain bacteria. This bacteria is known to grow exponentially initially. Below is a table of data showing the weight of the sample of bacteria over several hours of monitoring. ## Data Table | Time (in hours) | 1 | 2 | 3 | 4 | 5 | |-----------------|------|------|------|-------|-------| | Weight (in grams)| 46.00| 52.90| 60.84| ERROR | 80.45 | ## Questions ### (a) [C08] Calculate the hourly growth factor for the bacteria for the first three hours. *There is no given answer for this question.* ### (b) [C13] There was an error in the measurement at hour 4. What should the student expect the hour 4 weight of the sample to be? *There is no given answer for this question.* ## Additional Monitoring | Time (in hours) | 6 | 7 | 8 | 9 | 10 | |-----------------|------|-------|-------|-------|-------| | Weight (in grams)| 92.52| 106.40| 120.88| 134.16| 148.04| ### (c) [C15] The student notices that growth eventually stopped following an exponential model. At what hour did this happen? Answer: "Day 9 is when it stops." (This answer is marked incorrect.) ### (d) [C01] What could be a reason why the exponential growth eventually stops? Answer: "Because the bacteria could have been put in a new environment." (This answer is marked incorrect.) --- Note: The handwritten answers for questions (a), (b), (c), and (d) are marked with an "X," indicating they are incorrect. The correct interpretations are necessary to address these questions accurately.

USA. Benjamin Banneker (1731-1806) is one of the great American heroes of all time. The son and grandson of Africans captured and enslaved, he was fortunate to have been born free. He inherited the family farm where he worked hard all of his life. As a child he had a few months of schooling. Everything else he had to do on his own. He loved mathematics and science but did not get a chance to learn astronomy until he was in his fifties. Then he performed a near miracle, learning it all in less than a year. In his hand-written journal, he recorded two right triangle examples that interested him. You can solve them here and remember the great man who enjoyed geometry. On the page in his journal next to the August 1775 astronomy calculations, Banneker wrote, in the style of that time: Suppose a ladder 60 feet long be placed in a Street so as to reach a window on the one Side 37 feet high, and without moving it at bottom, will reach another window on the other side of teh Street which is 23…

For the remainder of this question, we will consider one of the world's most popular video games, Minecraft (adapted from Mills & Mills, 2016). In this game, the character (you) can attempt to tame a wolf with a bone. Assume that you get 9 tries to tame the wolf, i.e. there are 9 bones. Each time you tame the wolf, the wolf becomes a dog and a new wolf appears which you can then attempt to also tame. This continues until you have used up all 9 bones, and the goal is to end up with as many dogs as possible at the end of the game. The probability of taming the wolf with each attempt is fixed at 0.54. Let X denote the number of dogs at the end of the game so that X BIN (9,0.54). Assume you are about to play the game. 12. What is the probability you will tame less than 4 dogs?

A company produces widgets at plants 1 and 2. It costs 125x1y2 dollars to produce x units at plant 1 and 235x1y3 dollars to produce x units at plant 2.Each plant can produce up to 500 units. Each unit produced can be sold for $10. At most 800 widgets can be sold. Determine how -the company canmaximize its profit.