I think I need to go backward for my answers. starting with c. As I am no good at math I have to guess I am wrong. Can I get some guidence on how to set up the problem?
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 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.
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.
Ns = Number of animals in sample
As = Acres in sample
a.
Ns = k As
so k = Ns/As
b. k = 12/100 deer per acre = .12
c. N = k A is my assumption (the number of deer per acre is constant .12 just like in my sample)
so
N = .12 * 2500
N = 300
The stopping distance d of a car after the brakes have been applied varies directly as the square of the speed r. if the car traveling 70mph cab stop in 270ft, how many feet will it take the same car to stop when it 1s traveling 50 mph
To set up the problem, we can start by defining the variables involved:
Let:
- P be the total population of animals,
- S be the size of the habitat in acres, and
- k be the constant of variation that relates the population to the habitat size.
a. To write an equation using only one variable that could be used to solve for the constant of variation k, we can express the relationship between the population and the habitat size using the variable P:
P = k * S
Here, P is directly proportional to S, meaning that as the habitat size increases or decreases, the population will increase or decrease proportionally.
b. The biologist counted 12 white-tailed deer in a 100-acre parcel of land, which gives us the following information:
P = 12 (total population of animals)
S = 100 (habitat size in acres)
We can use this information to find the constant of variation k. Plugging the values into the equation from part a, we have:
12 = k * 100
To solve for k, we divide both sides of the equation by 100:
k = 12 / 100
k = 0.12
Therefore, the constant of variation (k) is 0.12.
c. If the entire nature preserve is 2,500 acres, we can use the constant of variation (k) we found in part b to calculate the total white-tailed deer population (P) in the preserve.
P = k * S
Plugging in the values:
k = 0.12 (constant of variation)
S = 2,500 (habitat size in acres)
P = 0.12 * 2,500
P = 300
Hence, the total white-tailed deer population in the preserve would be 300.