Question 585462
T(n)=a(1+r)^n


T(n)=24000(1+(-0.06))^n


T(n)=24000(1-0.06)^n


T(n)=24000(0.94)^n


So the formula is T(n)=24000(0.94)^n 



Now plug in T(n) = 24000/4 = 6000 and solve for n


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T(n)=24000(0.94)^n


6000=24000(0.94)^n


6000/24000=(0.94)^n


1/4=(0.94)^n


ln(1/4) = ln((0.94)^n)


ln(1/4) = n*ln(0.94)


ln(1/4)/ln(0.94) = n


n = ln(1/4)/ln(0.94)


n = 22.4046


So in roughly 22.4046 years, the population will be 1/4 of the current population.

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