It will take 12.8 years for the population to reach 1500.
The current population of the small town is 12000.
A small town's population is vanishing at a 15% annual rate.
So,
100 - 15 = 85% = 0.85
The population can be modeled with the following equation:
P( x ) = 12000 × ( 0.85 )ˣ
Where "x" is the number of years and P is the population. We want to find how long it will take before the population is equal to 1500, so we need to substitute P with 1500 and solve for x.
Therefore,
1500 = 12000 × ( 0.85 )ˣ
( 0.85 )ˣ = 1500 / 12000
( 0.85 )ˣ = 0.125
Taking logarithm on each side.
㏑ ( 0.85 )ˣ = ㏑ 0.125
x × ㏑ ( 0.85 ) = ㏑ 0.125
x = ( ㏑ 0.125 ) / ( ㏑ ( 0.85 ) )
x = ( - 2.07944 ) / ( - 0.162519 )
x = 12.79505
To reach the population of 500 people, it will take 12.8 years approximately.
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