In a study using 50 foreign-language vocabulary words, the learning rate L (in words per minute) was found to depend on the number of words already learned x, according to the equation . Use the intercepts to determine a window, and then use a graphing utility to graph the equation for Based on the graph, is the learning rate increasing or decreasing?
A) increasing
B) decreasing

Question

In a study using 50 foreign-language vocabulary words, the learning rate L (in words per minute) was found to depend on the number of words already learned x, according to the equation  . Use the intercepts to determine a window, and then use a graphing utility to graph the equation for  Based on the graph, is the learning rate increasing or decreasing? ​
A) increasing 
B) decreasing

Quizplus · Accepted Answer

To determine the window, we need to find the intercepts of the equation. 
Setting x=0, we get L=8. 
Setting L=0, we get e^(0.023x)-1=0, which gives x=0. 
Therefore, the window is (0, infinity) for x and (8, infinity) for L.

Using a graphing utility, we can graph the equation y=8(e^(0.023x)-1) for x in the range [0, 50]. 
The graph shows that the learning rate is decreasing, as the slope of the curve is decreasing and approaching zero as x increases.

In a Study Using 50 Foreign-Language Vocabulary Words, the Learning