Math
posted by Vanessa on .
The average student enrolled in the 20wk 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) = 2e0.02t
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.

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