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I have 5,66million people and it grows with 2% a year, how long does it take to get double the amount

 Feb 27, 2015

Best Answer 

 #1
avatar+118587 
+5

 

$$\\(5.66million)*2=(5.6million)*e^{0.02t}\\
2=e^{0.02t}\\
ln2=ln\;e^{0.02t}\\
ln2=0.02t * ln\;e\\
ln2=0.02t \\
t=\frac{ln2}{0.02}$$

 

$${\frac{{ln}{\left({\mathtt{2}}\right)}}{{\mathtt{0.02}}}} = {\mathtt{34.657\: \!359\: \!027\: \!997\: \!265\: \!5}}$$

 

34.66 years correct to 2 decimal places.

 Feb 27, 2015
 #1
avatar+118587 
+5
Best Answer

 

$$\\(5.66million)*2=(5.6million)*e^{0.02t}\\
2=e^{0.02t}\\
ln2=ln\;e^{0.02t}\\
ln2=0.02t * ln\;e\\
ln2=0.02t \\
t=\frac{ln2}{0.02}$$

 

$${\frac{{ln}{\left({\mathtt{2}}\right)}}{{\mathtt{0.02}}}} = {\mathtt{34.657\: \!359\: \!027\: \!997\: \!265\: \!5}}$$

 

34.66 years correct to 2 decimal places.

Melody Feb 27, 2015

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