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!