Question

in order to keep track of the elephant population in africa, kiara catches 82 elephants and marks them. later, kiara gets in a helicopter and takes pictures containing 184 elephants. of the elephants in the pictures, 23 are marked. to the nearest whole number, what is the best estimate for the elephant population?

Explanation:

Step1: Set up proportion

Let \( N \) be the total elephant population. The proportion of marked elephants in the sample should equal the proportion of marked elephants in the population. So, \(\frac{\text{marked in sample}}{\text{total in sample}}=\frac{\text{marked in population}}{\text{total in population}}\), which gives \(\frac{23}{184}=\frac{82}{N}\).

Step2: Cross - multiply and solve for \( N \)

Cross - multiplying the proportion \(\frac{23}{184}=\frac{82}{N}\) gives \(23N = 82\times184\). First, calculate \(82\times184 = 82\times(180 + 4)=82\times180+82\times4=14760 + 328 = 15088\). Then, solve for \(N\) by dividing both sides of the equation \(23N=15088\) by 23: \(N=\frac{15088}{23}\).

Step3: Calculate the value of \(N\)

\(\frac{15088}{23}=656\).

Answer:

656