bernard is a bird enthusiast and is trying to estimate the number of hawks living in his region. he traps…

bernard is a bird enthusiast and is trying to estimate the number of hawks living in his region. he traps 107 hawks and tags them. later, he traps 971 hawks, 39 of which are tagged. to the nearest whole number, what is the best estimate for the hawk population?

bernard is a bird enthusiast and is trying to estimate the number of hawks living in his region. he traps 107 hawks and tags them. later, he traps 971 hawks, 39 of which are tagged. to the nearest whole number, what is the best estimate for the hawk population?

Answer

Explanation:

Step1: Set up the proportion

Let $x$ be the total hawk population. The proportion is $\frac{\text{tagged hawks in first - catch}}{\text{total population}}=\frac{\text{tagged hawks in second - catch}}{\text{number of hawks in second - catch}}$, so $\frac{107}{x}=\frac{39}{971}$.

Step2: Cross - multiply

Cross - multiplying gives $39x = 107\times971$.

Step3: Calculate the right - hand side

$107\times971=107\times(900 + 70+1)=107\times900+107\times70 + 107\times1=96300+7490 + 107=103897$.

Step4: Solve for $x$

$x=\frac{103897}{39}\approx2664$.

Answer:

2664