Question

NO LINKS!!!
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

Answer:

t = 12 years

Step-by-step 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:

$\implies 5.510^{0.23t}=92$

$\implies \ln 5.510^{0.23t}= \ln 92$

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

$\implies t= \dfrac{\ln 92}{0.23 \ln 5.510}$

$\implies t=11.5201909...$

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

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