1. ## Help

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?

2. 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

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

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 $\displaystyle t$

Originally Posted by dc52789
bump
you are aware that bumping is against the rules, right?

3. Originally Posted by Jhevon
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?
I know that now.

4. ## This 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?

5. 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 $\displaystyle P(t) = 1000e^{0.588t}$, you can answer the rest of the questions

6. Originally Posted by Jhevon
yes. i suppose your professor requires 3 decimal places?

so now you know $\displaystyle P(t) = 1000e^{0.588t}$, you can answer the rest of the questions
Wow...that really helps a lot. Thanks.