Math Question

An entomologist has an insect colony for an experiment. The population of insects is increasing at a continuous rate of \( 4.5 \) percent per week. The initial population of the insect colony was 560 .
a. The function that models the insect population after \( t \) weeks is \( P(t)= \)
b. Using the function from part (a) we can estimate that the insect population after 7 weeks is
(round your answer to the nearest whole number)
c. After how many weeks will the population reach 9700 insects?
(round your answer to one decimal place)



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