The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1800 after 1 day, what is the size of the colony after three days? How long is it until there are 10000 mosquitoes?

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- Oct 25th 2008, 03:44 PMdc52789Help
The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1800 after 1 day, what is the size of the colony after three days? How long is it until there are 10000 mosquitoes?

- Oct 25th 2008, 04:35 PMJhevon
do you know what formula to use? the exponential growth formula

$\displaystyle P(t) = P_0 e^{rt}$

where $\displaystyle P(t)$ is the population after time $\displaystyle t$, $\displaystyle P_0$ is the initial population, and $\displaystyle r$ is the rate of growth.

you are told $\displaystyle P_0 = 1000$

you are also told $\displaystyle P(1) = 1800$. you can use that to find $\displaystyle r$. then you can fill in the unknowns in the formula above, except for $\displaystyle P(t)$ and $\displaystyle t$ of course.

you can then answer the other questions.

the size of the population after 3 days is given by $\displaystyle P(3)$.

to find out how long it takes the population to become 10000, set $\displaystyle P(t) = 10000$ and solve for $\displaystyle t$

you are aware that bumping is against the rules, right? - Oct 25th 2008, 04:38 PMdc52789
- Oct 25th 2008, 05:17 PMdc52789This is what I have so far
I was finding r so this is what I tried to do.

P(t) = Poe^rt

1800 = 1000e^(1)r

1.8 = e^1r

ln 1.8 = ln e^r

ln 1.8 = r

0.588 = r

Is this right?

- Oct 25th 2008, 05:19 PMJhevon
- Oct 25th 2008, 05:22 PMdc52789