For exponential decreasing, the formula is P(t)=P(0)e^-kt, where P(0)is the initial amount, k is the constant of decrease, and t is time. So:
1100=1900*e^-8k
0.57894736842105263157894736842105=e^-8k
ln 0.57894736842105263157894736842105=ln e^-8k=-8k ln e=-8k
k=0.06831796329600873949338548174034
So, the population reaches 100 in:
100/1900=e^-0.06831796329600873949338548174034t
0.05263157894736842105263157894737=e^-0.06831796329600873949338548174034t
ln 0.05263157894736842105263157894737=ln e^-0.06831796329600873949338548174034t=
-0.06831796329600873949338548174034t ln e=-0.06831796329600873949338548174034t
t=43.0990 years
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