To estimate the size of the bear population on the Keweenaw peninsula conservationists captured tagged and released 50 bears. One year later a random sample of 100 bears included only 2 tagged bears. What is the conservationist estimate of the size of the bear population?

let the number of bears be x

50/x = 2/100
2x = 5000
x = 2500

Thanks

To estimate the size of the bear population on the Keweenaw Peninsula, the conservationists used a method called tagging and recapture. Let's break down the steps to get the estimate:

1. Initially, the conservationists captured, tagged, and released 50 bears.
2. One year later, they took a random sample of 100 bears.
3. Out of the 100 bears in the sample, only 2 were tagged.

To estimate the size of the bear population, we can use a proportional relationship:

(Tagged animals in the initial capture) / (Total population) = (Tagged animals in the recapture) / (Size of the recaptured sample)

Let's apply that formula to our scenario:

50 (Tagged animals in the initial capture) / (Total population) = 2 (Tagged animals in the recapture) / 100 (Size of the recaptured sample)

Now, we need to rearrange the formula to solve for the total population:

Total population = (Tagged animals in the initial capture * Size of the recaptured sample) / Tagged animals in the recapture

Substituting the values from our scenario:

Total population = (50 * 100) / 2 = 2500

Therefore, based on this estimation method, the conservationists estimate the size of the bear population on the Keweenaw Peninsula to be 2500.