Question

Q5 Density 12 Points Scientists who are studying a new antibiotic have some bacteria in a petri dish. There is a dead region in the center of the dish (where the antibiotic has been applied) with a ring of bacteria around it. The inner boundary of the ring of bacteria is 1 cm from the center of the dish, and the bacteria extend from there to the outer edge of the dish. The dish has a total radius of 5 cm. The population density of bacteria at a distance r сm from the center of the petri dish is 5 -T 8(r)= millions of bacteria per cm², where 1 <r <5. Q5.1 Setting up the integral 7 Points On a separate sheet of paper, write an integral you will evaluate to find the total population of bacteria (be sure to include the limits of integration). Include a short explanation of how you got your integral. Feel free to use a clear, labelled figure if that will help you explain what you did.

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