You are running an experiment to determine the efficacy of an antibiotic that you helped to develop.

At 8 am, you introduce an antibiotic to a culture of 2400 bacteria. At

12 pm the culture contains 1500 bacteria.

1. Assume that the number of bacteria is decreasing by a constant amount each hour. (There is a linear relationship between the time passing and the number of bacteria in the culture.) LetN(t) be the number of bacteria, andt be the number of hours that have passed since the start of the experiment.

a. Find the equation that gives the number of bacteria as a function of the number of hours after the culture was started.

b. Sketch a graph of the equation, including the y and the x-intercept.

c. Interpret the graph. In writing, explain the meanings of the x and y-intercepts, and the slope in the context of this application. If you used this equation to find the number of bacteria in the culture at 8 pm, what answer would it give you? Does that make sense? Discuss the restrictions you would have to put on the domain of the function to keep you from getting meaningless answers.