Participants in a psychology experiment were able to memorize an average of M words in t minutes, where M = −0.001t3 + 0.1t2. Use the following graph.Estimate the number of words memorized after 14 min.
m
20 /
18 /
16 /
14 /
12 /
10 /
8 /
6 /
4 /
2/02468101214161820t
t = 14 min
M = −0.001 * t ^ 3 + 0.1 * t ^ 2
M = −0.001 * 14 ^ 3 + 0.1 * 14 ^ 2
M = −0.001 * 2744 + 0.1 * 196
M = - 2.744 + 19.6
M = 16.856 words
To estimate the number of words memorized after 14 minutes, we can use the graph to find the corresponding value on the y-axis (M) for t = 14.
Looking at the graph, we can see that there is a point on the graph where t = 14 and M is between 8 and 10.
To get a more accurate estimate, we can draw a horizontal line from t = 14 on the x-axis until it intersects with the graph. Then, draw a vertical line from this point of intersection until it intersects with the y-axis.
Based on the graph, it shows that the vertical line intersects the y-axis at a value slightly below 9. Hence, we can estimate that the number of words memorized after 14 minutes is approximately 9.