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A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 440 . (a) Find an expression for the number of bacteria after

`t`

hours. (Round the relative growth rate to four decimal places.)

`A(t)=`

(b) Find the number of bacteria after three hours. (Round your answer to the nearest whole number.) bacteria (c) Find the rate of growth after three hours. (Round your answer to four decimal places.) bacteria per hour (d) When will the population reach 10,000 ? (Round your answer to two decimal places.) hours