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# The population of a colony of a certain insect obeys the law of uninhibited growth. If there are 500 insects initially and there are 800 aft

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The population of a colony of a certain insect obeys the law of uninhibited growth. If there are 500 insects initially and there are 800 after one day, what is the size of the colony after 3 days?

Guest Mar 4, 2015

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$$\\P=500e^{kt}\\\\ 800=500e^{k*1}\\\\ 1.6=e^k\\\\ ln(1.6)=k\\\\ so\\\\ P=500e^{ln(1.6)*t}\\\\ when\;\; t=3\\\\ P=500e^{ln(1.6)*3}\\\\ P=500e^{3ln(1.6)}\\\\$$

$${\mathtt{500}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{\left({\mathtt{3}}{\mathtt{\,\times\,}}{ln}{\left({\mathtt{1.6}}\right)}\right)} = {\mathtt{2\,047.999\: \!999\: \!999\: \!999\: \!5}}$$

There will  be 2048 insects.

Melody  Mar 4, 2015
#1
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$$\\P=500e^{kt}\\\\ 800=500e^{k*1}\\\\ 1.6=e^k\\\\ ln(1.6)=k\\\\ so\\\\ P=500e^{ln(1.6)*t}\\\\ when\;\; t=3\\\\ P=500e^{ln(1.6)*3}\\\\ P=500e^{3ln(1.6)}\\\\$$

$${\mathtt{500}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{\left({\mathtt{3}}{\mathtt{\,\times\,}}{ln}{\left({\mathtt{1.6}}\right)}\right)} = {\mathtt{2\,047.999\: \!999\: \!999\: \!999\: \!5}}$$

There will  be 2048 insects.

Melody  Mar 4, 2015
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A population of insects obeys the law of uninhibited growth. If there are 650 insects to begin with, and there are 800 after 2 days, how many will theure be after 5 days?

Guest Nov 15, 2016