SOLUTION: a). Suppose a population is growing exponentially with p(0) = 1,000.000 and P(2) = 2,000.000. Find p(3) = ? b). Let f be a continuous on [0,2] and differentiable on (0,2). What

Algebra ->  Functions -> SOLUTION: a). Suppose a population is growing exponentially with p(0) = 1,000.000 and P(2) = 2,000.000. Find p(3) = ? b). Let f be a continuous on [0,2] and differentiable on (0,2). What      Log On


   

Question 999524: a). Suppose a population is growing exponentially with p(0) = 1,000.000 and P(2) = 2,000.000. Find p(3) = ?
b). Let f be a continuous on [0,2] and differentiable on (0,2). What does the Mean value Theorem state about f?
Thank you
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
P=Ae%5E%28bt%29
.
.
P%280%29=A=1000000
.
.
P%282%29=1000000e%5E%282b%29=2000000
e%5E%282b%29=2
2b=ln%282%29
b=ln%282%29%2F2
.
.
So then,
P%283%29=1000000e%5E%28%283%2F2%29ln%282%29%29
.
.
.
In the interval (0,2), there exists a value c where 0%3Cc%3C2 such that the derivative of the function at x=c is equal to,
%28df%2Fdx%29%28c%29=%28f%282%29-f%280%29%29%2F%282-0%29
%28df%2Fdx%29%28c%29=%28f%282%29-f%280%29%29%2F2