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

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) (Show Source): You can put this solution on YOUR website!

Integrate,

When t=0, p=1500.

At t=2 hours,

or approximately,

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