Question

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The number N of beavers in a given area after t years can be approximated by the following.
N = 5.510^0.23t), 0 ≤ t ≤ 9

Use the model to approximate how many years it will take for the beaver population to reach 92. (Round your answer to the nearest year.)
t= ________ years

Answer 1

t = 12 years

Explanation:

Given equation:

`N = 5.510^(0.23t), \quad 0 \leq t \leq 9`

where:

• N = number of beavers
• t = time (in years)

To approximate how many years it will take for the beaver population, N, to reach 92, substitute N = 92 into the given equation and solve for t:

`\implies 5.510^(0.23t)=92`

`\implies \ln 5.510^(0.23t)= \ln 92`

`\implies 0.23t\ln 5.510= \ln 92`

`\implies t= (\ln 92)/(0.23 \ln 5.510)`

`\implies t=11.5201909...`

`\implies t=12\; \rm years`

Therefore, it took 12 years (to the nearest year) for the beaver population to reach 92.