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# a countrys population in 1995 was 56 million.in 2002 it was 59 million.estimate the population in 2016 using exponential growth formula roun

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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.?

Guest Dec 10, 2014

#1
+26397
+10

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

.

Alan  Dec 10, 2014
Sort:

#1
+26397
+10

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

.

Alan  Dec 10, 2014

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