A bacterial culture in a petri dish grows at an exponential rate. The petr dish has an area of 256 $$ \mathrm{~mm}^{2} $$, and the bacterial culture stops growing when it covers this area. The area in $$ \mathrm{mm}^{2} $$ that the

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### Known Conditions:
1. The area of the petri dish is $$ A = 256 \, \mathrm{mm}^2 $$.
2. The bacterial culture grows at an exponential rate until it covers the entire area of the dish.

### General Approach:
1. **Exponential Growth Model**: The growth of the bacteria can be modeled by the equation:
   $$
   N(t) = N_0 e^{kt}
   $$
   where:
   - $$ N(t) $$ is the number of bacteria at time $$ t $$,
   - $$ N_0 $$ is the initial number of bacteria,
   - $$ k $$ is the growth constant,
   - $$ t $$ is time,
   - $$ e $$ is the base of the natural logarithm.

2. **Coverage Condition**: The culture stops growing when it covers the area of the petri dish, which is $$ 256 \, \mathrm{mm}^2 $$.

3. **Finding Time to Cover the Area**: If we know the initial number of bacteria and the growth constant, we can find the time $$ t $$ when the area is fully covered.

If you provide the initial number of bacteria $$ N_0 $$ and the growth constant $$ k $$, I can help you calculate the time $$ t $$ when the bacteria cover the area of the petri dish. Please provide the missing information or clarify your question!
To determine when the bacterial culture covers the entire petri dish area of $$ 256 \, \mathrm{mm}^{2} $$, use the exponential growth formula: $$ N(t) = N_0 e^{kt} $$ Where: - $$ N(t) $$ is the number of bacteria at time $$ t $$, - $$ N_0 $$ is the initial number of bacteria, - $$ k $$ is the growth constant, - $$ t $$ is time. Set $$ N(t) = 256 \, \mathrm{mm}^{2} $$ and solve for $$ t $$ using the known values of $$ N_0 $$ and $$ k $$.

A bacterial culture in a petri dish grows at an exponential rate. The petr dish has an area of 256 \( \mathrm{~mm}^{2} \), and the bacterial culture stops growing when it covers this area. The area in \( \mathrm{mm}^{2} \) that the

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