Graph the function over the interval t 0 40 How many days un

Graph the function over the interval t [0, 40]. How many days until only half the words are remembered? How does this compare to Exercise 77? How many days until only one-fifth of the words are remembered?

After 7 days, what is the average number of words retained? How many days until only 5 words can be recalled?

What is the significance of the horizontal asymptote (what does it mean in this context)?

Solution

a) 25 = (4t + 20)/t   =========> 25t = 4t + 20

21t = 20 ======> t = 20/21

Therefore, only half of the words are remembered after 20/21 days

b) 10 = (4t + 20)/t   ========> 10t = 4t + 20

t = 20/6 = 10/3

Therefore, one-fifth of the words are remembered after 10/3 days.

c) i) W(t) = (4*7 + 20)/7 = 48/7

Therefore, 48/7 is the average number

ii) 5 = (4t + 20)/t ======> 5t = 4t + 20

t = 20

Therefore, 5 words can be recalled after 20 days.

d) The horizontal asymptote signifes that you will never Forget 4 words that you memorized. This indicates that as time pass by, the number oF words you remember lessens but there are 4 words that you can never Forget.