The number $\mathrm{B}$ of bacteria in a petri dish culture after $\mathrm{t}$ hours is given by $\mathrm{B}=100 e^{0.693 \mathrm{t}}$. (a) What is the initial number of bacteria present? (b) How many bacteria are present after 6 hours? (a) The initial number of bacteria present is 100 . (Round to the nearest whole number as needed.) (b) There are bacteria present after 6 hours. (Round to the nearest whole number as needed.)

Step 1 ：The number of bacteria in a petri dish culture after t hours is given by the equation \(B=100 e^{0.693 t}\).

Step 2 ：We are asked to find (a) the initial number of bacteria present and (b) the number of bacteria present after 6 hours.

Step 3 ：(a) The initial number of bacteria present can be found by substituting t=0 into the given equation. This is because at t=0, it represents the initial state of the bacteria culture.

Step 4 ：Substituting t=0 into the equation gives \(B=100 e^{0.693 \times 0} = 100\).

Step 5 ：So, the initial number of bacteria present is \(\boxed{100}\).

Step 6 ：(b) The number of bacteria present after 6 hours can be found by substituting t=6 into the given equation.

Step 7 ：Substituting t=6 into the equation gives \(B=100 e^{0.693 \times 6} \approx 6394.35\).

Step 8 ：Rounding to the nearest whole number, there are \(\boxed{6394}\) bacteria present after 6 hours.