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**dc52789** · October 25th 2008, 03:44 PM

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?

**Jhevon** · October 25th 2008, 04:35 PM

Originally Posted by dc52789

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?

do you know what formula to use? the exponential growth formula

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

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

you are told $P_0 = 1000$

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

you can then answer the other questions.

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

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

Originally Posted by dc52789

bump

you are aware that bumping is against the rules, right?

**dc52789** · October 25th 2008, 04:38 PM

Originally Posted by Jhevon

do you know what formula to use? the exponential growth formula

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

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

you are told $P_0 = 1000$

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

you can then answer the other questions.

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

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

you are aware that bumping is against the rules, right?

I know that now.

**dc52789** · October 25th 2008, 05:17 PM

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?

**Jhevon** · October 25th 2008, 05:19 PM

Originally Posted by dc52789

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?

yes. i suppose your professor requires 3 decimal places?

so now you know $P(t) = 1000e^{0.588t}$ , you can answer the rest of the questions

**dc52789** · October 25th 2008, 05:22 PM

Originally Posted by Jhevon

yes. i suppose your professor requires 3 decimal places?

so now you know $P(t) = 1000e^{0.588t}$ , you can answer the rest of the questions

Wow...that really helps a lot. Thanks.

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