Problems [15 ate} 1. A certain apartment building, which you don't want to live in. opened in 1994. In 1996. the number at mice infecting that building was 2. In 1999. there were 32 mice. Let M represent the number of mice in years since 1995. (6.5 pts) a. Find the equation that models M as a linear function of t. (2 pts) b. Write M as an exponential function of t. What are the parameters of interest and what do they tell us about the growth in the number at mice over time? (2 pts) c. What is the predicted number of mice in the building in 2000 based on the linear model? What about with the exponential model? It, in 2000. the actual number of mice observed turns out to be 172. calculate residual values to determine which model seems to be a more reliable predictor of the data. Explain how you know which model is more reliable. (2.5 pts) 2. The table below shows the typical mass of eight sea animals. (8.5 pts) a. Plot and label these values on a log scale. (2.5 pts) Killer whale 5,937 Bluen tuna 534 BowenoW m m m 102 10-1 10 10' 1o2 103 10" 105 103 b. If an average human is 1.91 orders of magnitude lighter than a Killer whale, what is the weight of an average human in kg? (2 pt) How many times larger is a Killer whale than a Maui 's dolphin? (2 pt) d. How many orders of magnitude larger is a Killer whale than a Maui's dolphin? (2 pt) .0