Q. 112 - Precalculus Enhanced with Graphing Utilities

Question

Suppose that a student has $500$ vocabulary words to learn. If the student learns $15$ words after $5$ minutes, the function:

$L\left(t\right)=500\left(1-e^{-0.0016t}\right)$

approximates the no. of words L that the student will learn after t minutes.

Part (a): How many words will the student learn after $30$ minutes?

Part (b): How many words will the student learn after $60$ minutes?

Step-by-Step Solution

Answer

Part (a):$84$ is the number of words the student will learn after $30$ minutes.

Part (b):$153$is the number of words the student will learn after $60$ minutes.

Part (a) Step 1: Determine no. of words the student learns after 30 minutes.

Consider the given function,

$L\left(t\right)=500\left(1-e^{-0.0016t}\right)$

Assume t to be the time in minutes.

Substitute $t=30$ in the given function,

$$\begin{gathered} L\left(30\right)=500\left(1-e^{-0.0016\times 30}\right) \\ =83.61 \\ \approx 84 \end{gathered}$$

Part (b) Step 1: Determine no. of words the student learns after 60 minutes.

Consider the given function,

$L\left(t\right)=500\left(1-e^{-0.0016t}\right)$

Assume t to be the time in minutes.

Substitute $t=60$in the given function,

$$\begin{gathered} L\left(60\right)=500\left(1-e^{-0.0016\times 60}\right) \\ =153.24 \\ \approx 153 \end{gathered}$$