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December 13th, 2017, 05:58 AM  #1 
Newbie Joined: Jan 2014 Posts: 17 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, 08:36 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,692 Thanks: 1351 
I would say the "back of the book" solution is incorrect ... I agree with yours.

December 13th, 2017, 10:04 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,378 Thanks: 730 
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! 
December 14th, 2017, 08:36 AM  #4 
Newbie Joined: Jan 2014 Posts: 17 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, 10:37 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,378 Thanks: 730 
Ask your teacher...


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