Psychologists sometimes use the function L(t)=A(1-e^-kt) to measure the amount L learned at time t minutes.

Question

The number A represents the amount to be learned, and the number k measures the rate of learning. Suppose that a student has an amount A of 200 vocabulary words to learn. A psychologist determines that the student learned 20 vocabulary words after 5 minutes.

A) Determine the rate of learning k.

B) Approximately how many words will the student have learned after 10 minutes?

C) How long does it take for the student to  learn 180 words?

Answer 1

Given L( t ) = 

Where A is amount to be learned

k is  rate of learning

t is time in minits 

Given a student learned 20 vocabulary words after 5 minutes means 

-5k = ln(0.9)

-5k = - 0.1053

k = 0.02107

Rate of learning k is 0.02107

 

b)Now we have to find number words in 10minits

number words learned in 10minits is 38 words

 

c)Now we have to calculate time taken for 180 words

-tk = ln(0.1)

We know value of k = 0.02107

-t × 0.02107 = -2.302

t = 109.28 min

So  time taken for 180 words is 109.28 min