SDS 302: Homework 10 (20 points) Excel (4 pts) Using the dataset from the Linear Pre-lab, answer the following question: Is a linear model appropriate for modeling the life expectancy in Iraq in terms of years since 1990? As part of your answer, copy and paste a scatterplot with linear model and a residual plot from Excel, then interpret the parameters of the linear model and describe if a linear model is appropriate or not referencing the plots and statistics from Excel to support your conclusion. Problems (16 pts) 1. Researchers date a new fossil using Carbon-14, which has a half-life of 3,257 years. For a particular fossil, they observed that 35% of the original amount of Carbon-14 had already decayed. How old is this fossil? (3 pts) 2. The population of a certain type of bird is limited by its nesting capacity. The maximum number of birds which can nest is 6750 and the initial number of birds in the population was 250. After one year the bird population was 375. The researchers want to model this population using a logistic model with t in terms of years. a) Find the value for the parameter k. (3 pts) b) When will population growth begin to slow down? (1 pt) c) How many birds will there be when the growth begins to slow down? (1 pt) 3. Suppose the CDC was tracking the daily spread of a stomach virus according to a logistic model with 16 people initially affected on a cruise ship of 5000 people. If there were 250 people infected at the end of the third day, how many days would it take until 2,000 were infected? (3 pts) 4. The table below shows the typical mass of eight sea animals. a) Plot and label these values on a log scale. (2 pts) b) If an average human is 1.93 orders of magnitude lighter than a Killer whale, what is the weight of an average human in kg? (1 pt) c) How many times larger is a Killer whale than a Maui's dolphin? (1 pt) d) How many orders of magnitude larger is a Killer whale than a Maui's dolphin? (1 pt) Animal Blue whale Killer whale Bluefin tuna Bottlenose dolphin Maui's dolphin Flounder Starfish Spongebob Squarepants Copyright 2017 Department of Statistics and Data Sciences. All rights reserved. Body mass (kg) 190,000 5,987 684 650 40 6.8 5 0.02