Imagine that at a particular time, a kitchen counter has on it 20 bacteria and that this type of bacteria doubles in number every 10 minutes. The exponential function A(t)=20e0.06931t is a good model for predicting the number of bacteria, A(t), in the population t minutes from some particular start time. How many bacteria could be predicted to be on the counter 2.5 hours later? (Round to 2 decimal places.) also...
The sociologists Stephan and Mishler found that the exponential function N ( p ) = N 1 e^ − .11( p − 1 ) for 1 ≤ p ≤ 10 is produced when members of a discussion group of 10 people are ranked according to the number of times each participated. N 1 represents the number of times the first-ranked person participated. If, in a discussion group of 10 people, the first-ranked person participated 40 times, how many times did the fourth-ranked person participate? (Round to 2 decimal places.)
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When a particular amount of money P , called the principal, is invested at the interest rate r and is compounded n times a year, the amount A accumulated after t years is A ( t ) = P (1+ r/n )^nt Determine the amount of money accumulated after 10 years if $ 5,000 is invested in an account that pays 10% interest compounded monthly. Round to the nearest cent.
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Let us model the number of automobile sales in a developing country as N ( t ) = 154000/ 1 + 5.9e^−0.3( t−2010), t ≥ 2010 Where N is the number of automobiles sold in one year and t is this year. Round all answers to the nearest car.
a . How many cars were sold in 2010 , the first year of observation?
b . How many cars are projected to be sold in the year 2020 ?
c . If the model holds well into the future, at what level will the sale of cars stabilize?