which of the following describes the function shown in the table below?\n| x | y |\n| -4 | 16 |\n| -1 | 2…

which of the following describes the function shown in the table below?\n| x | y |\n| -4 | 16 |\n| -1 | 2 |\n| 2 | 0.25 |\n| 4 | 0.0625 |\n| 5 | 0.03125 |\nexponential, there is a continual rate of growth\nexponential, there is a continual rate of decay or decrease\nquadratic, there is a second degree change in the y - values\nquadratic, there is a constant difference between consecutive y - values

which of the following describes the function shown in the table below?\n| x | y |\n| -4 | 16 |\n| -1 | 2 |\n| 2 | 0.25 |\n| 4 | 0.0625 |\n| 5 | 0.03125 |\nexponential, there is a continual rate of growth\nexponential, there is a continual rate of decay or decrease\nquadratic, there is a second degree change in the y - values\nquadratic, there is a constant difference between consecutive y - values

Answer

Explanation:

Step1: Check for exponential - growth/decay

Find the ratio of consecutive $y$-values. For example, when going from $x=-4,y = 16$ to $x=-1,y = 2$, the ratio is $\frac{2}{16}=\frac{1}{8}$. When going from $x=-1,y = 2$ to $x = 2,y=0.25$, the ratio is $\frac{0.25}{2}=\frac{1}{8}$. Since the ratio of consecutive $y$-values is constant ($r=\frac{1}{8}<1$), it is an exponential function.

Step2: Determine growth or decay

Since the common ratio $r=\frac{1}{8}<1$, the function is an exponential decay function.

Step3: Check for quadratic

For a quadratic function, the second - differences of the $y$-values should be constant. Calculate the first - differences: From $y(-4)=16$ to $y(-1)=2$, the difference is $2 - 16=-14$. From $y(-1)=2$ to $y(2)=0.25$, the difference is $0.25 - 2=-1.75$. The first - differences are not constant, so it is not a quadratic function.

Answer:

exponential, there is a continual rate of decay or decrease