what is the rate of change of the function described in the table?\n\\( \\frac { 12 } { 5 } \\)\n5\n\\(…

Explanation:

Step1: Recall the formula for rate of change in an exponential function

For an exponential function (y = ab^{x}), the rate of change (common ratio) can be found by (\frac{y_{n + 1}}{y_{n}}).

Step2: Calculate the ratio using two consecutive (y -)values

Take (y(0)=\frac{1}{2}) and (y(1)=\frac{5}{2}). Then (\frac{y(1)}{y(0)}=\frac{\frac{5}{2}}{\frac{1}{2}}). Using the rule (\frac{a/b}{c/d}=\frac{ad}{bc}), we have (\frac{5/2}{1/2}=\frac{5\times2}{2\times1}=5). We can check with another pair: (y(1)=\frac{5}{2}) and (y(2)=\frac{25}{2}). (\frac{y(2)}{y(1)}=\frac{\frac{25}{2}}{\frac{5}{2}}=\frac{25\times2}{2\times5}=5).

Answer:

(5)