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Kenneth Rosen Edition 7 Exercise 2.4 Question 7 (Page No. 168)
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Find at least three different sequences beginning with the terms $1, 2, 4$ whose terms are generated by a simple formula or rule.
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FIRST SEQUENCE
$a_{n}=2^{n-1}$ where n=1,2,3,4......
SECOND SEQUENCE
$a_{n}=2a_{n-1},a_{1}=1$
THIRD SEQUENCE
$a_{n}=a_{n-1}+a_{n-2},a_{1}=1,a_{2}=2$
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Kenneth Rosen Edition 7 Exercise 2.4 Question 22 (Page No. 168 - 169)
An employee joined a company in $2009$ with a starting salary of $\$50,000.$ Every year this employee receives a raise of $\$1000$ plus $5\%$ of the salary of the previous year. Set up a recurrence relation for the ... of this employee be in $2017?$ Find an explicit formula for the salary of this employee $n$ years after $2009.$
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Kenneth Rosen Edition 7 Exercise 2.4 Question 21 (Page No. 168)
A factory makes custom sports cars at an increasing rate. In the first month, only one car is made, in the second month, two cars are made, and so on, with $n$ cars made in the $nth$ month. Set up a recurrence ... in the first year? Find an explicit formula for the number of cars produced in the first $n$ months by this factory
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Kenneth Rosen Edition 7 Exercise 2.4 Question 20 (Page No. 168)
Assume that the population of the world in $2010$ was $6.9$ billion and is growing at the rate of $1.1\%$ a year. Set up a recurrence relation for the population of the world $n$ years after $2010.$ Find an explicit formula for the population of the world $n$ years after $2010.$ What will the population of the world be in $2030?$
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Kenneth Rosen Edition 7 Exercise 2.4 Question 19 (Page No. 168)
Suppose that the number of bacteria in a colony triples every hour. Set up a recurrence relation for the number of bacteria after n hours have elapsed. If $100$ bacteria are used to begin a new colony, how many bacteria will be in the colony in $10$ hours?
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