A bacteria culture grows with constant relative growth rate. The bacteria count was $400$ after $2$ hours and $15625$ after $6$ hours. Answer the following questions.

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1. What is the relative growth rate?
Answer: $k =$

2. What was the initial size of the culture?
Answer: $P_0 =$

3. Find an expression for the number of bacteria after $t$ hours.
Answer: $P(t)=$

4. Find the number of cells after $4$ hours.
Answer:

5. When will the population reach $1000000?$
Answer (in hours): $t =$

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