If B = number of bacteria, then you can solve the equation by plugging in the numbers you know and finding k. "e" is 2.718.....there is a button on scientific calculators which will give you the precise value of "e".

Your last sentence contains B and t. Use those to find k in your equation B = 1000e^kt

To reduce the powers of your equation, use a natural log function (ln)
i.e. to find k in the equation B = e^k take the (ln) of both side which yields ln B = k