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.
k=d(deer)/a(acres)
b. A biologist counted the number of white tail deer in a 100 acre parcel of land in a nature preserve and found 12 deer. Find the constant of variation k.
k=12/100=.12 per acre
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.
.12=d/2,500
2,500(.12)=d
d=300
If the constant k is .12 deer per acre and we multiply it by 2,500 acres, then we can find the total popullation.
Are these correct? Thanks for the help.
In the derivation of the equation perhaps starting with
d = ka (d is number of deer, a is number of acres)
then the given : 12 deer per 100 acres
12 = k(100)
k = .12
so your equation would be
d = .12a
your arithmetic and your answer is fine
Yes, your answers and explanations are correct!
For part (a), you correctly set up the equation using only one variable, which is "k," the constant of variation. In this case, "k" represents the number of deer (d) per acre (a). So the equation is k = d/a.
For part (b), you used the given information that there were 12 deer in a 100-acre parcel of land. By substituting these values into the equation from part (a), you correctly found that k = 12/100 = 0.12 deer per acre.
For part (c), you correctly used the value of k that you found in part (b), which is 0.12 deer per acre. By multiplying this value by the total number of acres in the nature preserve (2,500), you correctly calculated that the total white-tail deer population in the preserve is 300.
Well done! Keep up the good work!