Jessica has been tracking the population of a town. the population was 8,230 last year and has been increasing by 1.25 times each year. how can jessica develop a function to model this
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The formulae to model this population is :
N(t) = Ae^-kt
Where A is a constant and in this case the initial population which 8230.
Given that the population increases by 1.25 times we can get the value of k.
At time 1 :
1.25 = e^ -k × 1
Taking ln on both sides we have :
ln 1.25 = ln (e ^ - k)
0.2231 = - k
At this point t = 1
Thus :
0.2231 = - k
k = 0.2231
Rewriting the formulae :
N(t) = 8230e^0.2231t
This formula can be used to model the population.
N(t) = Ae^-kt
Where A is a constant and in this case the initial population which 8230.
Given that the population increases by 1.25 times we can get the value of k.
At time 1 :
1.25 = e^ -k × 1
Taking ln on both sides we have :
ln 1.25 = ln (e ^ - k)
0.2231 = - k
At this point t = 1
Thus :
0.2231 = - k
k = 0.2231
Rewriting the formulae :
N(t) = 8230e^0.2231t
This formula can be used to model the population.
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