# Help

• Oct 25th 2008, 03:44 PM
dc52789
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?
• Oct 25th 2008, 04:35 PM
Jhevon
Quote:

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\$

Quote:

Originally Posted by dc52789
bump

you are aware that bumping is against the rules, right?
• Oct 25th 2008, 04:38 PM
dc52789
Quote:

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.
• Oct 25th 2008, 05:17 PM
dc52789
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?
• Oct 25th 2008, 05:19 PM
Jhevon
Quote:

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
• Oct 25th 2008, 05:22 PM
dc52789
Quote:

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.