Question

which scenario would be best modeled by a quadratic function? the path of a plane traveling from kansas city to washington, dc. the equation for radioactive decay, $a = a_0cdot(12)^{\frac{t}{h}}$. the population of bacteria growing in a petri dish in a high school biology class. the population of elk in yellowstone national park after all the wolves have disappeared.

Explanation:

Step1: Analyze each option

Quadratic functions are of the form $y = ax^{2}+bx + c$ ($a
eq0$) and often model parabolic - shaped paths or relationships.

1. The path of a plane traveling from Kansas City to Washington, DC is a straight - line path (assuming no detours) and is best modeled by a linear function.
2. The equation for radioactive decay $A = A_{0}\cdot(12)^{\frac{t}{h}}$ is an exponential function, not a quadratic function.
3. The population of bacteria growing in a petri dish in a high - school biology class often follows an exponential growth model (at least initially) $P(t)=P_{0}e^{rt}$, not a quadratic function.
4. The population of elk in Yellowstone National Park after all the wolves have disappeared may follow a pattern where the population initially grows due to lack of predators, but then may face resource limitations. This can be modeled by a quadratic function in some cases as the growth is not linear or exponential indefinitely and may have a parabolic - like behavior due to factors such as carrying capacity.

Answer:

the population of elk in Yellowstone National Park after all the wolves have disappeared