Polynomial Function and Exponential Growth
Date: 06/08/99 at 22:39:29 From: roland relevo Subject: Polynomials Dear Dr. Math, I have a homework question for my alegbra class. Here goes: Find a polynomial function with integer coefficients that has 3, 2, -4 and -1 as zeroes. All I know is that it is fourth degree polynomial. Help! Here's another one. A story problem: A colony of bacteria of 175000 is discovered in a petri dish. The colony doubles in size every 2.45 seconds. Model the population using exponential growth. What is the population 20 seconds after it is discovered? How long will it take to reach 3.5 billion? Where do I begin? Sincerely, Roland R.
Date: 06/09/99 at 10:16:21 From: Doctor Rob Subject: Re: Polynomials Thanks for writing to Ask Dr. Math! For the first problem, use this fact: If r is a root of a polynomial, then x-r is a factor. That should give you four factors of the polynomial. For your second question, in the time from 0 to t seconds there are t/2.45 units of 2.45 seconds each. After each one, you have multiplied the population by 2, so the formula for the number of bacteria should be 175000 * 2^(t/2.45) There's your start. Another approach is to say that the formula for exponential growth is P = a * b^t for some constants a and b. Then when t = 0, P = a = 175000, and when t = 2.45, P = 2*a, so b^2.45 = 2, and you can solve for b. - Doctor Rob, The Math Forum http://mathforum.org/dr.math/
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