No calculators show work let Pt represent the number of peop

No calculators, show work: let P(t) represent the number of people (in millions) after t years. a.) write a function for a population which decays 6% every 3 years. You may use Po to represent the population at year t=0. b.) find the half-life of the population from part (a.). You can leave your answer exact, as it should contain logarithms in it.

Solution

Solution;

It is given that populoation

Given initial population

P(t) = P_o e^kt

decays 6% every 3 years

thus

P(3) = amount left = P_o - 0.06P_o

   = P_o (1-0.06)

= 0.94P_o

Now for k

0.94P_o = P_o e^3K

   e^3k= 0.94

k = ln(0.94)/3

therefore function for number of people P(t) = P_o e^{(ln(0.94)/3)t}

(b)

at half life t/2

population P(t) = P₀/2

P₀/2 = P_o e(ln(0.94)/3)t/2

t = 67.21 years

Answer