1. ## World population...

hey guys,

I hate to keep bugging you all but I'm having some difficulties with this question. It's annoying because I followed my notes exactly and still got the answer wrong.

Here's the question:

The table gives estimates of the world population, in millions, from 1750 to 2000.

Year Population
1750 790
1800 980
1850 1260
1900 1650
1950 2560
2000 6080

(a) Use the exponential model and the population figures for 1750 and 1800 to predict the world population in 1900 and 1950.

This is what I attempted:

So, 1750: 790 mil and 1800: 980 mil

P(t) = P(o) * e^kt
980 = 760 * e^k(50) because 1800-1750 = 50 years
980/760 = e^k(50)
1.289 = e^k(50)

ln(1.289)/50 = k
0.005=k (0.5%)

so, P(t) = 760 * e^0.005t

Then, to solve for 1900:

P'(150)=760*e^0.005(150) * 0.005 (note: 150 comes from 1900-1750 = 150 years in between - I'm following what my prof. did, and this is what he did so...)
P'(150)=8 million

I'm not sure what I'm doing wrong. I know that 8 mil is way too low (or, at least it seems like it compared to all the other values that the table gave).

Any help's appreciated! Thanks.

2. What you found is the rate of change of the population per year. To find the population itself, we simply find the value of $P(t)$ at $t=150$:

$P(150)=760e^{0.005\cdot150}.$