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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.In a certain year,27% of adults in a certain country viewed a college education as essential for success. For the following ten-year period, this percentage increased by approximately 2.6percent each year. The percentage of adults from this country who viewed a college education as essential for success x years after the first year can be represented by ________.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?
- On the average, 26 patrons per year come to the I.U.library to borrow the I Ching (assume that interarrival timesare exponential). Borrowers who find the book unavailableleave and never return. A borrower keeps a copy of the IChing for an average of 4 weeks.a If the library has only one copy, what is the expectednumber of borrowers who will come to borrow the IChing each year and find that the book is not available?b Suppose that each person who comes to borrow theI Ching and is unable to is considered to cost the library$1 in goodwill. A copy of the I Ching lasts two yearsand costs $11. A thief has just stolen the library’s onlycopy. To minimize the sum of purchasing and goodwillcosts over the next two years, how many copies of the IChing should be purchased?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.Suppose that all car owners fill when their tanks are exactly half full. At the present time, an average up of 7.5 customers per hour arrive at a single-pump gas station. It takes an average of 4 minutes to service a car. Assume that interarrival and service times are both exponential. For the present situation, compute L and W.Suppose that a gas shortage occurs and panic buying takes place. To model the phenomenon, suppose that all car owners now purchase gas when their tanks are exactly three quarters full. Now each car owner will fill up trice as often. Since each car owner is now putting less gas into the tank during each visit to the station, we assume that the average service time has been reduced to 2 1/2 minutes. How has panic buying affected L and W?
- My dog just had 3 frisky puppies who jump in and outof their whelping box. A puppy spends an average of 10minutes (exponentially distributed) in the whelping boxbefore jumping out. Once out of the box, a puppy spends anaverage of 15 minutes (exponentially distributed) beforejumping back into the box.a At any given time, what is the probability that morepuppies will be out of the box than will be in the box? b On the average, how many puppies will be in thebox?One article states that each one-second delay in loading search results has the effect of multiplying the probability that an online customer will make a purchase by 0.90.† Let P denote the probability, as a percentage, that an Amazon customer will make a purchase if the search results require t seconds to load. Suppose that at the time a customer initiates a search for flatware, the probability that she will make a purchase is 50%. Make an exponential model that shows the percentage probability P as a function of t. P(t) =A certain radioactive isotope has a half-life of 5 days. If one is to make a table showing the half-life decay of a sample of this isotope from 32 grams to 1 gram; list the time (in days, starting with t = 0) in the first column and the mass remaining (in grams) in the second column, which type of sequence is used in the first column and which type of sequence is used in the second column?