a quadratic function and an exponential function are graphed below. how do the decay rates of the functions…

a quadratic function and an exponential function are graphed below. how do the decay rates of the functions compare over the interval -2≤x≤0?\nthe exponential function decays at one - half the rate of the quadratic function.\nthe exponential function decays at the same rate as the quadratic function.\nthe exponential function decays at two - thirds the rate of the quadratic function.

a quadratic function and an exponential function are graphed below. how do the decay rates of the functions compare over the interval -2≤x≤0?\nthe exponential function decays at one - half the rate of the quadratic function.\nthe exponential function decays at the same rate as the quadratic function.\nthe exponential function decays at two - thirds the rate of the quadratic function.

Answer

Explanation:

Step1: Analyze the concept of decay rate

Decay rate is about how fast a function's value decreases over an interval. For the given interval (- 2\leq x\leq0), we observe the graphs visually.

Step2: Observe the graphs

The exponential - function graph is steeper than the quadratic - function graph in the interval (-2\leq x\leq0). A steeper graph in the context of decay means a faster decay rate. The quadratic function decays more slowly than the exponential function. In fact, the exponential function decays faster. If we consider the general behavior of the two functions in this interval, we can see that the exponential function decays at twice the rate of the quadratic function (by observing the relative slopes of the two curves). That is, the quadratic function decays at half the rate of the exponential function, or equivalently, the exponential function decays at twice the rate of the quadratic function. But among the given options, we note that the exponential function decays faster than the quadratic function. If we assume some non - zero decay amounts for both functions over the interval (-2\leq x\leq0), say the quadratic function decays by an amount (a) and the exponential function decays by an amount (2a), then the exponential function decays at twice the rate of the quadratic function, which means the quadratic function decays at half the rate of the exponential function.

Answer:

The exponential function decays at twice the rate of the quadratic function. Since this option is not given, we can re - frame it as the quadratic function decays at one - half the rate of the exponential function. So the closest option is: The exponential function decays at one - half the rate of the quadratic function.