We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
568
3
avatar

In 2012, the growth of rate of the south african population was -0,412% Determine the population of South Africa in 2011 if the population was 48, 810, 427 in 2012

 Jul 29, 2015

Best Answer 

 #1
avatar+27664 
+10

Rate of growth is dN/dt = -0.412/100*N which can be solved to get  Nt = N12*e-0.412/100*t where N12 = 48810427.  (I've assumed the -0.412% means -0.412% per year)

 

So, to find N11 (the number  in 2011) we set t = -1 (i.e. it's 1 year earlier) to get:

 

$${\mathtt{N11}} = {\mathtt{48\,810\,427}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{{\mathtt{\,-\,}}\left({\frac{{\mathtt{0.412}}}{{\mathtt{100}}}}{\mathtt{\,\times\,}}\left(-{\mathtt{1}}\right)\right)} \Rightarrow {\mathtt{N11}} = {\mathtt{49\,011\,940.792\: \!604\: \!870\: \!237\: \!79}}$$

 

or N11 ≈ 49011941

.

 Jul 29, 2015
 #1
avatar+27664 
+10
Best Answer

Rate of growth is dN/dt = -0.412/100*N which can be solved to get  Nt = N12*e-0.412/100*t where N12 = 48810427.  (I've assumed the -0.412% means -0.412% per year)

 

So, to find N11 (the number  in 2011) we set t = -1 (i.e. it's 1 year earlier) to get:

 

$${\mathtt{N11}} = {\mathtt{48\,810\,427}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{{\mathtt{\,-\,}}\left({\frac{{\mathtt{0.412}}}{{\mathtt{100}}}}{\mathtt{\,\times\,}}\left(-{\mathtt{1}}\right)\right)} \Rightarrow {\mathtt{N11}} = {\mathtt{49\,011\,940.792\: \!604\: \!870\: \!237\: \!79}}$$

 

or N11 ≈ 49011941

.

Alan Jul 29, 2015
 #2
avatar
+5

Thank you so much Alan ^_^ 

 Jul 29, 2015
 #3
avatar+100169 
+5

Thanks Alan  

 

Hi anon, you probably already realize this but the growth rate is negative so the population is declining - not actually growing.   

 Jul 29, 2015

5 Online Users