SOLUTION: The number of bacteria p in a pond after t hours is p(t). The more bacteria there are, the more rapidly the number increases. This is expressed by the equation p'(t)= 2p(t) . Find

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Question 256916: The number of bacteria p in a pond after t hours is p(t). The more bacteria there are, the more rapidly the number increases. This is expressed by the equation p'(t)= 2p(t) . Find the most general exponential function of the form A*e^Kt which satisfies the equation. (A and K are constants. Hint: substitute this function into the equation and see what you get).
p(t)=
If there were 1500 bacteria at t=0, how many are there 2 hours later?
p(2)=

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
dp%2Fdt=2p
dp%2Fp=2dt
Integrate,
ln%28p%29=2t%2BC
p=Ce%5E%282t%29
When t=0, p=1500.
p%28t%29=1500e%5E%282t%29
At t=2 hours,
p%28t%29=1500e%5E%282%282%29%29=1500e%5E%284%29
or approximately,
p=81897