A bacteria culture starts with 500 bacteria and doubles in size every half hour. Suppose

the population grows exponentially.

(a) Find an exponential function

P

(

t

) that models the population of bacteria

t

hours

after the initial bacteria culture is introduced.

(b) How many bacteria are there after 5 hours?

(c) Estimate the time it will take for the bacteria population to reach 200,000.