Question

A researcher studies the generality of plant and ant species on Mount Wilhelm in Papua New Guinea. Generality is the number of plant species per ant species. The generality can be model by the function

g(x) = 0.000004x^2 - 0.0119x + 10.605, where x is the elevation (in meters). At what elevation(s) do you expect to find a generality of 3 plant species per ant species? Round your answers to the nearest thousandth place.

Answer 1

To find the elevation levels at which there are 3 plant species per ant species, we solve the quadratic equation 0.000004x^2 - 0.0119x + 10.605 = 3 by using the quadratic formula and then round the solutions to the nearest thousandth.

Step-by-step explanation:

The student is asking to solve the quadratic equation g(x) = 0.000004x^2 - 0.0119x + 10.605 for g(x) = 3. This means we need to find the value of x (the elevation in meters) where the generality is 3 plant species per ant species. We can solve this by setting the equation equal to 3 and solving for x:

0.000004x^2 - 0.0119x + 10.605 = 3

Now we subtract 3 from both sides to set the equation to zero:

0.000004x^2 - 0.0119x + 7.605 = 0

Using the quadratic formula, x = (-b ± √(b^2 - 4ac))/(2a), where a = 0.000004, b = -0.0119, and c = 7.605, we can find the values of x that satisfy this equation.

After calculating, round the answers to the nearest thousandth place as requested.