Question : basic integration question

Hi

The rate of change of a population is given in terms of 1000s of individuals per year. The initial population size was 100,000. I had to work out the increase in population after 15 year period and the answer I got was 175. I think this answer is right as I checked in on wolfram alpha. Anyhow does this mean the population change was actually 175 000 and the total population after 15 years was 100,000 + 175,000 = 275 000. The book says the answer is 175,000 but that doesnt seem right.

thanks

Answer : basic integration question

In http:#33329334 you state a problem where you are looking for the total population after 15 years (not the increase in population).

dp(t)/dx = (4+0.15t)^(3/2)
dp(t) = (4+0.15t)^(3/2) dx

Integrating from 0..15:
Delta p = p(15) - p(0) = 175.08
So, 175.08K represents the increase in the frog population in 15 years.
p(0) = 100K (initial condition)
p(15) = 175.08 + p(0) = 275.08K = total frog population in year 2015

Since the book said "Estimate the population", I interpret that to mean "Estimate the total population ". If that is the book's interpretation, then the book's answer of 175K is wrong. If the book's author interpreted it instead as "Estimate the increase in population", then the book's answer is right.

I hope you never have to take a multiple choice test written by the book's author.

The good news for you is that with so many ambiguities in the book, this really makes you think hard about what you are modeling; and this is likely to give you a deeper understanding of word problems.

Maybe the author plugged in the formulas real quick into an integrator and copied the 175 at t=15 forgetting that the left hand side of the integral yields Delta P = P(15) - P(0).