Question

the number of words per minute that an average person can type is given by the function ( w(t)=60 - 26e^{-0.3t} ), where ( t ) is the time in minutes after the
(a) find ( w(0) ).
( w(0)= ) (round to the nearest whole number as needed.)
(b) find ( w(1) ).
( w(1)= ) (round to the nearest whole number as needed.)
(c) find ( w(4) ).
( w(4)= ) (round to the nearest whole number as needed.)
(a) find ( w(12) ).
( w(12)= ) (round to the nearest whole number as needed.)

Explanation:

Step1: Identify the function

The function is given as \( W(t) = 60 - 26e^{-0.3t} \), where \( t \) is the time in months. We need to find \( W(12) \), so we substitute \( t = 12 \) into the function.

Step2: Substitute \( t = 12 \) into the function

Substitute \( t = 12 \) into \( W(t) \):

$$ W(12) = 60 - 26e^{-0.3 \times 12} $$

Step3: Calculate the exponent

First, calculate the exponent: \( -0.3 \times 12 = -3.6 \)

Step4: Calculate \( e^{-3.6} \)

Using a calculator, \( e^{-3.6} \approx 0.0273237 \)

Step5: Calculate \( 26e^{-3.6} \)

Multiply 26 by \( e^{-3.6} \):

$$ 26 \times 0.0273237 \approx 0.710416 $$

Step6: Calculate \( W(12) \)

Subtract this value from 60:

$$ W(12) = 60 - 0.710416 \approx 59.289584 $$

Step7: Round to the nearest whole number

Rounding 59.289584 to the nearest whole number gives 59.

Answer:

59