The population of a bacterial colony t hours after observation begins is found to be changing at the rate dP/dt = 200e^0.1t+150e^-0.03t. If the population was 200,000 bacteria when observations began, what will the population be 12 hours later?
what i did:
(1/12-0)[antiderivative 200e^0.1t+150e^-0.03t]
(1/12)[(200/1.1)e^1.1t + (150/0.97)e^0.97t]
(1/12)[((200/1.1)e^13.2 + (150/0.97)e^11.64) - ((200/1.1)e^0 + (150/0.97)e^0)]
9650594.820
is this right?? seems like a big number!
I don't know where you get the 1 and 12 from, if you assume the time observations began is time 0 your limits are 12 and 0.
You've also got the integration wrong, when talking about exponentials we do not add 1 to the power: which can be shown by taking the derivative using the chain rule