a countrys population in 1995 was 56 million.in 2002 it was 59 million.estimate the population in 2016 using exponential growth formula round to the nearest million.?
Use N = 56ek*t where t is the time in years from 1995 and k is an. as yet, unknown rate constant.
Find k from the 2002 data: 59 = 56ek*7 (because 2002 - 1995 = 7)
Divide through by 56, take logs, then divide by 7 to get k = ln(59/56)/7
$${\mathtt{k}} = {\frac{{ln}{\left({\frac{{\mathtt{59}}}{{\mathtt{56}}}}\right)}}{{\mathtt{7}}}} \Rightarrow {\mathtt{k}} = {\mathtt{0.007\: \!455\: \!107\: \!595\: \!795\: \!7}}$$
In 2016 t = 2016 - 1995 = 21, so
N = 56e0.007455*21
$${\mathtt{N}} = {\mathtt{56}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{\left({\mathtt{0.007\: \!455}}{\mathtt{\,\times\,}}{\mathtt{21}}\right)} \Rightarrow {\mathtt{N}} = {\mathtt{65.490\: \!604\: \!574\: \!065\: \!260\: \!8}}$$
or N ≈ 65 million
.
Use N = 56ek*t where t is the time in years from 1995 and k is an. as yet, unknown rate constant.
Find k from the 2002 data: 59 = 56ek*7 (because 2002 - 1995 = 7)
Divide through by 56, take logs, then divide by 7 to get k = ln(59/56)/7
$${\mathtt{k}} = {\frac{{ln}{\left({\frac{{\mathtt{59}}}{{\mathtt{56}}}}\right)}}{{\mathtt{7}}}} \Rightarrow {\mathtt{k}} = {\mathtt{0.007\: \!455\: \!107\: \!595\: \!795\: \!7}}$$
In 2016 t = 2016 - 1995 = 21, so
N = 56e0.007455*21
$${\mathtt{N}} = {\mathtt{56}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{\left({\mathtt{0.007\: \!455}}{\mathtt{\,\times\,}}{\mathtt{21}}\right)} \Rightarrow {\mathtt{N}} = {\mathtt{65.490\: \!604\: \!574\: \!065\: \!260\: \!8}}$$
or N ≈ 65 million
.