Question

L(t) = A(1- e^(-kt))
to measure the amount , L, learned at time, t. 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

Answer 1

information given: A = 200 and when t = 5, L = 20

so L = 200(1 - e^(-kt))

when t = 5, L = 20:

20 = 200(1 - e^(-5k))

thus 1 - e^(-5k) = 1/10

thus e^(-5k) = 9/10

thus -5k = ln(9/10)

thus k = -1/5*ln(9/10)

Answer 2

so 21.07?

Answer 3

can it be a negative?

Answer 4

the value of k is positive. you'd hope so, anyway...a negative value of k indicates that you're un-learning things

Answer 5

heheh i see can you do one more? approximately how many words will the student have learned after 15 minutes? "i plug in the formula but cant seem to get the math right

Answer 6

the value of L when t = 15:

L = 200(1 - e^(-15k))

simply substitute the value of k from before, and put that into a calculator

it should be less than 20

Answer 7

it should be more right since youre learning more words over time?

Answer 8

i put it in the calculator and get 200 which is wrong. how can i correct it? thanks for your help