Use the graph representing bacteria decay to estimate the domain of the function and solve for the average rate of change across the domain ,A.[tex]0 \leqslant y \leqslant 80, - 0.6875[/tex]B.[tex]0 \leqslant y \leqslant 80, - 1.45[/tex]C.[tex]0 \leqslant x \leqslant 55, - 1.45[/tex]D.[tex]0 \leqslant x \leqslant 55, - 0.6875[/tex]​

Answer:C. [tex]0\le x\le55,-1.45[/tex]Step-by-step explanation:The domain of the function refers to all values of x for which the function is defined.From the diagram the graph of the function exist on the interval [tex]x=0[/tex] to [tex]x=55[/tex].The average rate of change is the slope of the secant line joining the points (0,f(0)) and (55,f(55)).The average rate of change of this function f(x) on this interval is [tex]\frac{f(55)-f(0)}{55-0}[/tex]From the graph, [tex]f(0)=80[/tex] and [tex]f(55)=0[/tex].The average rate of change becomes:[tex]\frac{0-80}{55-0}=\frac{-80}{55}=-1.45[/tex] to the nearest hundredth.The correct answer is: C