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.

26.44 years since the begginig of the study.

Step-by-step explanation:

The populations of bears can be described by:

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

where t is in years.

we want to find t such:

5000*2^(-0.05*t) = 2000

2^(-0.05*t) = 2000/5000 = 2/5

then we use the rule:

a^y = x

then:

y = logₐ(x)

we use it in our equation and get:

2^(-0.05*t) = 2/5

-0.05*t = log₂(2/5) = ln(2/5)/ln(2)

t = ln(2/5)/ln(2) /-0.05 = 26.44

so 26.44 years since the begginig of the study.

d

step-by-step explanation: