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
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
.
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
.