Katya is a ranger in a nature reserve in Siberia, Russia, where she studies the changes in the reserve's bear population size over time. She found that the number of bears, B, in the reserve at t years since the beginning of the study can be modeled by the following function: B (t) = 5000*2^ (-0.05t) How long will it take the bear population in the reserve to get to 2000 bears? Round your answer, if necessary, to 2 decimal places.

Question

Mathematics

Emmanuel Hess

26 February, 03:42

Katya is a ranger in a nature reserve in Siberia, Russia, where she studies the changes in the reserve's bear population size over time. She found that the number of bears, B, in the reserve at t years since the beginning of the study can be modeled by the following function: B (t) = 5000*2^ (-0.05t) How long will it take the bear population in the reserve to get to 2000 bears? Round your answer, if necessary, to 2 decimal places.

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Lauryn Steele · Answer 1

B (t) = 5000 * 2^ (-0.05t)

2000 = 5000 * 2^ (-0.05t), div by 5000

0.4 = 2^ (-0.05t), ln on both sides = >

ln0.4 = (-0.05t) * ln2

(ln0.4) / ln2) / (-0.05) = t

t = 26.43

After 27 years