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## Homework Statement

A bacteria culture starts with 1000 bacteria and grows to a population of 7000 after an hour.

a) Find the size of the population after t hours.

b) Find the size of the population after 3 hours.

c) Find the rate of growth of the population after 3 hours.

d) When will the population reach 10 000?

## Homework Equations

y = yoe[itex]^{kt}[/itex]

## The Attempt at a Solution

**a)**y = yoe[itex]^{kt}[/itex]

7000 = 1000e[itex]^{kt}[/itex]

7 = e[itex]^{kt}[/itex]

ln7 = kt

ln7/t = k (is this it?)

**b)**y = yoe[itex]^{kt}[/itex]

y = 1000e[itex]^{k(2)}[/itex] (am I on the right track?)

**c)**I know I have to take the derivative but what do I take the derivative of?

**d)**No idea.

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