# Math

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The average student enrolled in the 20-wk Court Reporting I course at the American Institute of Court Reporting progresses according to the rule below where 0 t 20, and N'(t) measures the rate of change in the number of words/minute dictation the student takes in machine shorthand after t wk in the course.
N '(t) = 2e-0.02t
Assuming that the average student enrolled in the course begins with a dictation speed of 45 words/minute, find an expression N(t) that gives the dictation speed of the student after t weeks in the course.

• Math -

n=INT n'= 100e^.02t +C

I assume your e-.02t should have been e^.02t

Now find C. You know 45=100e^0+C, so solve for C

• Math -

N '(t) = 2e-0.02t
N = (2/-.02) e^-.02t + c
N = -100 e^-.02t + c
when t=0 , N = 45

45 = -100(1) + c
c = 145

N = -100 e^-.02t + 145

testing:
if t = 0
N = -100 e^0 +145
= 45 , good

if t = 5
N = -100 e^-.1 + 145
= -90.5 + 145
= 54.5 , improving

if t = 20
N = 78 , looks logical, and my answer is reasonable.

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