Homework3-Exponential.Induction

# Homework3-Exponential.Induction - ITI 111 Dr Kantor...

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ITI 111 Homework 3 Dr. Kantor Homework: Exponentials and Mathematical Induction 1. Suppose that each person who gets a message relays it to 5 other people, and that this takes 5 minutes. [Be careful: If we start at time “0” with only one person knowing, how many people will know at the end of 5 minutes? Let’s call that point “the end of the first step”] How long would it take to reach all of the 50,000 people associated with Rutgers? Hint: If , , using logarithms? x y a how can we find x a. log(50,000) b. 6*log(50,000)/log(5) c. 5* log(50,000)/log(6) d. 5* log(50,000) e. 6*5*log(50,000) 2. How many people would each person have to call, if they keep calling, so that by the 5 th step they would have spread a message to more than 50,000 people? [The easiest way to solve this is to try several answers, and find the smallest one that gives more than 50,000 people at the 5 step.] a. 6 b. 7 c. 8 d. 9 e. 10 3. Chain reaction. In a nuclear explosion each atom that explodes causes some additional ones to explode. But of course, it does not explode again. It only explodes once. If each atom causes 2 others to explode, so that in the first step there is one exploding, then in second step 2 are exploding, and in the third step 4 are exploding, What is the formula for the number, p E that are exploding in an arbitrary step number p?

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Homework3-Exponential.Induction - ITI 111 Dr Kantor...

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