SOLUTION: Find the average value of the function f(t)=100e^(-0.5t) over the interval [0, 4]

Algebra ->  Functions -> SOLUTION: Find the average value of the function f(t)=100e^(-0.5t) over the interval [0, 4]      Log On


   

Question 1079601: Find the average value of the function f(t)=100e^(-0.5t) over the interval [0, 4]
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Integrate the function over the range and divide by the length of the range.
A=int%28f%28t%29%2Cdt%2C0%2C4%29%2F%284-0%29
So,
int%28100e%5E%28-0.5t%29%2Cdt%2C0%2C4%29=-200e%5E%28-0.5%29%2BC
int%28100e%5E%28-0.5t%29%2Cdt%2C0%2C4%29=-200e%5E%28-2%29%2B200e%5E%280%29
int%28100e%5E%28-0.5t%29%2Cdt%2C0%2C4%29=200-200%2Fe%5E%282%29
A=50-50%2Fe%5E%282%29
A=50%281-1%2Fe%5E%282%29%29