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 Differential Equations Ordinary and Partial Differential Equations Math Forum

 December 13th, 2017, 04:58 AM #1 Newbie   Joined: Jan 2014 Posts: 19 Thanks: 0 Solution Below is a question from my textbook. Question: The size of the population of a small town changes at a rate directly proportional to the population present at time t (in years) . The initial population of 10 000 people increases by 15% in 3 years. What will be the population after 10 years. My Answer: $\displaystyle dp/dt=kp, p(0)=10000, p(3)=11500$. $\displaystyle p(t)=10000(1.15)^{t/3}$. $\displaystyle p(10)\approx15934$ people. Am I right? However, the answer at the back of my textbook is $\displaystyle p(10)\approx462163$ people.
 December 13th, 2017, 07:36 AM #2 Math Team     Joined: Jul 2011 From: Texas Posts: 2,949 Thanks: 1555 I would say the "back of the book" solution is incorrect ... I agree with yours. Thanks from woo
 December 13th, 2017, 09:04 AM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 I would have thought that this is the intent: 10000 to 15000, 3 years: rate = r: r = 15000/10000)^(1/3) - 1 = ~.1447 Then, over 10 years: 10000(1 + r)^10 = ~38634 Anyhooooo, answer at back of book is ridiculous! Thanks from woo
 December 14th, 2017, 07:36 AM #4 Newbie   Joined: Jan 2014 Posts: 19 Thanks: 0 Solution $\displaystyle P(10)\approx15934.04849$. Should I round the answer up to 15935 people or round down to 15934 people?
 December 14th, 2017, 09:37 AM #5 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Ask your teacher...

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