Chapter 3.2, Problem 128E

To determine

To calculate: the number of months it would take for the average score in Example $10$ to decrease to $60$ , using a graphing calculator.

Explain the method of solving the problem.

Describe another way to use the graphing utility to determine the answer.

Based on the shape of the graph, explain whether the rate at which a student forgets information increase or decrease with time.

Answer to Problem 128E

By using a graphing utility table feature, it can be concluded that in approximately $11$ months the average score decreases to $60$

Another method to solve the problem is by graphing a line $y=60$ in the same viewing window and finding the point of intersection of the two graphs.

Based on the shape of the graph, the rate at which students forgets information decreases, which may be due to consecutive retests.

Explanation of Solution

Given information:

Consider the information given in Example $10$ .

The human memory model to determine the average score of the students every month after the exam:

  $f(t)=75-6\ln (t+1)$

Where t is the time in months.

As per the problem.

The function:

  $f(t)=75-6\ln (t+1)$

Use graphing utility to graph the function.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press $\boxed{\text{Y=}}$ button.

Step 3: Enter the expression, $f(t)=75-6\ln (t+1)$ , which is required to graph.

Step 4: Press GRAPH button to graph the functions.

  

The table of values from the graph:

  

From the graph, it can be concluded that in approximately $11$ months the average score decreases to $60$

Another method to solve the problem is by graphing a line $y=60$ in the same viewing window as the function and finding the point of intersection of the two graphs.

  

The graph shows the two lines intersect at $(11.182,60)$ .

The function $f(t)=75-6\ln (t+1)$ has a decreasing graph.

Based on the shape of the graph, the rate at which students forgets information decreases, which may be due to consecutive retests.