1. The NCAA basketball tournament begins with 64 teams, and after each round, half the teams are eliminated. The number of remaining teams t(n) is an exponential function the number n of rounds already played.

A pizza restaurant has two phone lines for taking delivery orders. An average of 40 people per hour try to call the restaurant, and the average length of a phone call is 1 minute. If a person attempts to call when both lines are busy, he/she hangs up and is lost to the system. Assume that the time between people attempting to call and service times are exponential. a. What fraction of the time will both lines be free? What fraction of the time will both lines be busy? What fraction of the time will exactly one line be free? b. On the average, how many lines will be busy? c. On the average, how many callers will hang up each hour?

The rabbit population of Springfield, Ohio was 144,000 in 2016. It is expected to decrease by 7.2% per year. Use an exponential decay function to approximate the population in 2036 to the nearest hundredth

In the week that ended on January 4, there were 24 cases of flu reported in a city's hospital. In the 5 weeks that followed, the number of new cases reported each week had grown exponentially and can be modeled by this graph. 140 120 100 80 60 40 (1, 36)| 20 T(0, 24). 1 2 weeks since January 4 1. Which expression represents the number of cases of flu x weeks after January 4? Explain what each number in your chosen expression means in terms of the flu cases. а. 24-12" b. 24•(1.5)x с. 24 + 12x d. 24•(1.5)" 2. If the trend continued, would the number of cases reported be greater than 300 after 5 weeks? Explain or show how you know. flu cases reported

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Value of log2 32+ log₂ 16, will be.

Find the value of log 611• log 1116 • log 1621• log 21 26 • log 2631• log 3136.

Four months after it stops advertising, a manufacturing company notices that its sales have dropped from 100,000 units per month to 80,000 units per month. The sales follow an exponential pattern of decline. What will the sales be after another 2 months?