Chapter 5.3, Problem 112AYU

a.

To determine

To find:

(a) How many words will the student have learned after 30 minutes?

Answer to Problem 112AYU

Solution:

a) 420

Explanation of Solution

Given:

  $L\left(t\right)= 500\left(1-e^{-0.061t}\right)$

(a) How many words will the student have learned after 30 minutes?

  $L\left(t\right)= 500\left(1-e^{-0.061\left(30\right)}\right)$

  $L\left(t\right)= 500\left(1-e^{-1.83}\right)$

  $L\left(t\right)= 500\left(1-0.1604\right)$

  $L\left(t\right)= 500\left(0.8396\right)$

  $L\left(t\right)= 419.79$

  $L\left(t\right)\approx 420$

b.

To determine

To find:

(b) How many words will the student have learned after 60 minutes?

Answer to Problem 112AYU

Solution:

b) 487

Explanation of Solution

Given:

  $L\left(t\right)= 500\left(1-e^{-0.061t}\right)$

(b) How many words will the student have learned after 60 minutes?

  $L\left(t\right)= 500\left(1-e^{-0.061\left(60\right)}\right)$

  $L\left(t\right)= 500\left(1-e^{-3.66}\right)$

  $L\left(t\right)= 500\left(1-0.02573\right)$

  $L\left(t\right)= 500\left(0.9743\right)$

  $L\left(t\right)= 487.13$

  $L\left(t\right)\approx 487$