+0  
 
0
248
2
avatar

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

Best Answer 

 #1
avatar+91436 
+5

 

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

 

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

 

There will  be 2048 insects.   

Melody  Mar 4, 2015
Sort: 

2+0 Answers

 #1
avatar+91436 
+5
Best Answer

 

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

 

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

 

There will  be 2048 insects.   

Melody  Mar 4, 2015
 #2
avatar
0

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

21 Online Users

avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details