Chapter 1.8, Problem 71PS

Solution

To calculate: The elevation (s) at which 10 species of ants would be expected to find if the modeled function $S=-0.000013E^2+0.042E-21$ , where E is the elevation (in meters) and S is the number of ants species.

The elevations at which 10 species of ants is expected to be found is 1141 meters or 2090 meters.

Given information:

The modeled function is $S=-0.000013E^2+0.042E-21$ .

Formula used:

Use the quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ .

Calculation:

Write the model function:

  $S=-0.000013E^2+0.042E-21$

Substitute the S as 10,

  $10=-0.000013E^2+0.042E-21$

Subtract 10 from both sides,

  $\begin{array}{c}10-10=-0.000013E^2+0.042E-21-10\\ 0=-0.000013E^2+0.042E-31\end{array}$

Apply the quadratic formula,

  $\begin{array}{c}E=\frac{-0.042\pm \sqrt{{\left(0.042\right)}^2-4\left(-0.000013\right)\left(-31\right)}}{2\left(-0.000013\right)}\\ E=\frac{-0.042\pm \sqrt{0.001764-0.001612}}{-0.000026}\\ E=\frac{-0.042\pm \sqrt{0.000152}}{-0.000026}\\ E\approx 1141\text{or}E\approx 2090\end{array}$

Therefore, the expected elevation is about 2090 meters or 1141 meters.