compare the key features of the graphs of m(t) and s(t) within the context of the problem, including y…

Explanation:

Step1: Identify y - intercepts

Find the value of the functions at (t = 0). For (M(t)) and (S(t)), the y - intercept is the percentage of correct words at the start ((t=0)). Check the graphs of (M(t)) and (S(t)) at (t = 0) to get the initial values.

Step2: Find intersection points

Set (M(t)=S(t)) and solve for (t) within the domain (0\leq t\leq12). Graphically, this is where the two graphs cross. If there are no algebraic equations given, estimate from the graph.

Step3: Analyze function behavior

Observe if (M(t)) and (S(t)) are increasing, decreasing or constant over different intervals in (0\leq t\leq12). For example, if the graph is going up, the function is increasing.

Step4: Calculate rate of change

The rate of change of a function (y = f(t)) over the interval ([a,b]) is (\frac{f(b)-f(a)}{b - a}). For (M(t)) and (S(t)) over (0\leq t\leq12), calculate (\frac{M(12)-M(0)}{12 - 0}) and (\frac{S(12)-S(0)}{12 - 0}) respectively. Compare these two values.

Answer:

The y - intercepts give the starting percentages of correct words. Intersection points show when Michael and Sara have the same percentage of correct words. Function behavior shows improvement or decline over time. The rate of change calculations for (M(t)) and (S(t)) over (0\leq t\leq12) will show which one has a steeper increase (or decrease) in the percentage of correct words. Provide specific values from the graph for the y - intercepts, intersection points (estimated if needed), and calculated rate - of - change values for evidence.