functkon p(x)=80-30 log 2 x models percentage P(x) of students who can recall....

Question

important features of a classroom lecture as a function of​ time, where x represents the number of days that have elapsed since the lecture was given. The figure shows the graph of the function. After how many days do only

two-fifths of the students recall the important features of the classroom​ lecture? let P(x)=40 and solve for x.

After how many days do only two-fifths of the students recall the important features of the classroom​ lecture?

Answer 1

Hi Elle! I am glad to help you out!

First, let's make ourselves clear on what the variables mean. From the problem, we can see that p(x) is the percent of students who can recall lecture content, and x is the number of days after the lecture. We want to know the number of days x such that the retention rate (or p(x)) is p(x) = 40. So this means that to find x, we need to substitute 40 into p(x) and solve for x! Let's get started!

Note: When I state log2 (x), I mean to state 2 as the base subscript and x as the log argument!

p(x) = 40 = 80 - 30 * log2 (x) [Subtract 80 and then divide by -30]

4/3 = log2 (x) [Remember that logs can always be rewritten in terms of exponential expressions!]

Recall that logA (B) = C ⇒ A ^ C = B

Using this same logic then, log2 (x) = 4/3 ⇒⇒⇒ 2 ^ (4/3) = x ≈ 2.52 days <<<<< (ANSWER)

Hope this helped you! Ask me more questions if you like!

Answer 2

WE have P(x) = 2/5 = 40% and we have to find x:

xe have equation 40 = 80 - 30log2x from here log2x = 4/3, 2x = 10^4/3, x = 10^4/3/2 = 10.8 days