The Population of a Particular Country Has a Doubling Time

Question

Examlex · Accepted Answer

The Answer is From equation (2.7) the constant a can be determined from the doubling time as

t _ { D } = \frac { \ln 2 } { a }

so

a = \frac { 1 n 2 } { t _ { D } }

For

t _ { \mathrm { D } } = 45

years then

a = \frac { 0.693 } { 45 } = 0.0154 \mathrm { y } ^ { - 1 }

From equation (2.4) the quantity of any time is given in terms of the initial value as

N ( t ) = N _ { 0 } \exp ( a t )

so solving for

t

we get

t = \frac { 1 } { a } \ln \left( \frac { N ( t ) } { N _ { 0 } } ight)

for

N ( t ) = 3 N _ { 0 }

then we get

t = \left( \frac { 1 } { 0.0154 \mathrm { y } ^ { - 1 } } ight) \ln ( 3 ) = 71.3 ext { y ears }

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