The average student enrolled in the 20-week Court Reporting I course at the Amer

Question

The average student enrolled in the 20-week Court Reporting I course at the American Institute of Court Reporting progresses according to the rule

N'(t) = 2e0.02t    (0 t 20)

where N'(t) measures the rate of change in the number of words/minute of dictation the student takes in machine shorthand after t weeks in the course. Assuming that the average student enrolled in this course begins with a dictation speed of 80 words/minute, find an expression N(t) that gives the dictation speed of the student after t weeks in the course.

Explanation / Answer

given N'(t) = 2e0.02t

the average student enrolled in this course begins with a dictation speed of 80 words/minute =>N(0)=88-

N(t)= N'(t) dt

N(t)= 2e0.02t dt

N(t)= (-2/0.02)e0.02t +c

N(t)= -100e0.02t +c

given N(0)= 80

80= -100e0.02*0+c

80= -100+c

c=100+80

c=180

N(t)= -100e0.02t +180

dictation speed of the student after t weeks in the course.N(t)= -100e0.02t +180

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.