11 The population of a city is 51,000 and is decreasing at a rate of 1.75% per year. Use an exponential function to find the expected population in 5 years. Round to the nearest whole number. 12
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- The life (years), of a battery is approximately exponentially distributed with decay parameter of 0.2. Suppose this type of battery has a warranty period of 4 years. What is the probability that the battery will need to be replaced within the warranty period? 2. How long do you expect the battery to last?Suppose COVID-19, a pandemic that spread worldwide has infected 40,000 people on August 2020. Each day, the number of infected is estimated to be 300. Assuming that the number of daily infections are constant, 1. What is the monthly growth rate of infection k? Assume time t is measured in months. 2. How many persons will be confirmed positive by the end of December 2020? 3. Assuming that there has a turn of events and a vaccine is discovered by September 2020. In addition, the number of cases dropped with the number of recoveries at a rate of 100 per day. There have been no additional cases after September. How much time t will elapse for the cases of COVID-19 to drop to 500?Show that if a random variable has an exponentialdensity with the parameter θ, the probability that it willtake on a value less than −θ · ln(1 − p) is equal to p for 0 Fp < 1.
- The analysis of tooth shrinkage byC. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuingto decrease and that the evolutionary process has not yetcome to a halt. In northern Europeans, for example, tooth sizereduction now has a rate of 1% per 1000 years. In about how many years will human teeth be 90% of their present size?After constant complaints about the long wait from his customers, Ryan - the owner of shop - hasdecided to hire a second mechanic to handle installations. Customers, who arrive at a rate ofabout 3 per hour (Poisson), will wait in a single line until one of the two mechanics is free. Eachmechanic can serve about four customers per hour (Exponential).Do you think the improvement on customer experience will be significant? Computethe key waiting line characteristics BEFORE and AFTER the second mechanic is hired tosupport your answer.The analysis of tooth shrinkage byC. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuingto decrease and that the evolutionary process has not yetcome to a halt. In northern Europeans, for example, tooth sizereduction now has a rate of 1% per 1000 years. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?
- The analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is con-tinuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years. a. If t represents time in years and y represents tooth size, use the condition that y = 0.99y0 when t = 1000 to find the value of k in the equation y = y0 ekt. Then use this value of k to answer the following questions. b. In about how many years will human teeth be 90% of their present size? c. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?With the gasoline time series data from table 17.1, show the exponential smoothing forecasts using a = .1.a. applying the MSe measure of forecast accuracy, would you prefer a smoothing constant of a = .1 or a = .2 for the gasoline sales time series?b. are the results the same if you apply Mae as the measure of accuracy?c. What are the results if Mape is used?Consider the following (actual real-world) data of total cumulative coronavirus cases diagnosed in the United States by the following days: Sunday, 3/15 -- 3613 Monday, 3/16 -- 4596 Tuesday, 3/17 -- 6344 Wednesday, 3/18 -- 9197 Thursday, 3/19 -- 13779 Friday, 3/20 -- 19367 Saturday, 3/21 - 24192 Sunday, 3/22 - 33592(a) Does this data suggest exponential growth in the total number of cases diagnosed as function of the number of days that have elapsed? Explain how you would use the data to support your conclusion. (b) Let P(t) denote the total number of people in the US who have tested positive for the coronavirus on or before t days after March 15. Let P0=3613, the total number of people in the US who had tested positive for coronavirus by March 15. Then if we use an exponential growth model, P(t)=P0ekt, how would you use the above data to estimate the value of k? (c) Based on this data alone , how many total coronavirus cases would you expect to be diagnosed in the United States by…