The number S of ant species in K Cyn can be modeled by the function S = -0.000013E squared + 0.042E - 21 where E is the elevation (in meters). Predict the elevation(s)at which you would expect to find 10 species of ants.
To predict the elevation(s) at which you would expect to find 10 species of ants, we need to solve the given function for E when S is equal to 10.
The given function is: S = -0.000013E^2 + 0.042E - 21
Substituting S = 10 into the equation, we get:
10 = -0.000013E^2 + 0.042E - 21
Now, we need to solve this quadratic equation for E. First, let's rearrange the equation to standard quadratic form:
0.000013E^2 - 0.042E - 11 = 0
To solve this quadratic equation, we can use the quadratic formula:
E = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 0.000013, b = -0.042, and c = -11. Plugging these values into the formula, we get:
E = (-(-0.042) ± √((-0.042)^2 - 4 * 0.000013 * -11)) / (2 * 0.000013)
Simplifying further:
E = (0.042 ± √(0.0017644 + 0.000572)) / 0.000026
E = (0.042 ± √0.0023364) / 0.000026
Calculating the square root:
E = (0.042 ± 0.0483) / 0.000026
Simplifying:
E = (0.042 + 0.0483) / 0.000026 or E = (0.042 - 0.0483) / 0.000026
E = 3,558.46 meters or E = -303.08 meters
Therefore, we expect to find approximately 10 species of ants at an elevation of 3,558.46 meters or at an elevation of -303.08 meters. However, since elevation cannot be negative, we can conclude that you would expect to find 10 species of ants at an elevation of 3,558.46 meters.