A bacteria culture starts with `100` bacteria and grows at a rate proportional to its size. After `2` hours there will be `200` bacteria.

(a) Express the population `P` after `t` hours as a function of `t`. Be sure to keep at least 4 significant figures on the growth rate.
`P(t)`=  

(b) What will be the population after 7 hours?
  bacteria

(c) How long will it take for the population to reach 1570? Give your answer accurate to at least 2 decimal places.
  hours

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