4. To estimate animal populations, biologists count the total number of animals

Question

4. To estimate animal populations, biologists count the total number of animals in a small section of a habitat. The total population of animals is directly proportional to the size of the habitat (in acres) polled.

a. Write an equation using only one variable that could be used to solve for the constant of variation k.
b. A biologist counted 12 white tail deer in a 100-acre parcel of land in a nature preserve. Find the constant of variation k.
c. If the entire nature preserve is 2,500 acres, then what is the total white tail deer population in the preserve? Describe how you arrived at your answer.

Explanation / Answer

Let's abbreviate the number of animals as N. Let's abbreviate the number of acres as A. a. N = k A. The equation has TWO variables. I don't see how you could use only one variable. Notice that the problem said "directly proportional". That means if one variable increases, the other increases also. These problems always use multiplication (k times A in this problem). b. 12 = k (100). So k = 12/100 = 0.12 If your teacher wants to see all the units: 12 deer = k (100 acre). k = 12 deer/100 acre = 0.12 deer/acre c. N = (0.12 deer/acre)(2500 acre) = 300 deer

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