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December 13th, 2017, 04:58 AM   #1
woo
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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.
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December 13th, 2017, 07:36 AM   #2
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I would say the "back of the book" solution is incorrect ... I agree with yours.
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December 13th, 2017, 09:04 AM   #3
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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!
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December 14th, 2017, 07:36 AM   #4
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Solution

$\displaystyle P(10)\approx15934.04849$. Should I round the answer up to 15935 people or round down to 15934 people?
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December 14th, 2017, 09:37 AM   #5
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Ask your teacher...
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