During a research experiment, it was found that the number of bacteria in a culture grew at a rate proportional to its size. At
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a. See the attachment for a graph.
b. The value of y changes by -1.5 for each increase in x of 1. That means the relationship is linear and the slope is -1.5. If we "back up" one in the value of x to make it 0, we add 1.5 to the corresponding value of y to make it 15.00. This tells us the y-intercept is 15 and the equation can be written in slope-intercept form as
... y = -1.5x + 15
c. The slope means each bus ride costs $1.50. The intercept is the cost of the ticket: $15.00.
d. The x-intercept of the graph is 10. This means the ticket has no value left after 10 rides. Barry can use his card to ride the bus 10 times.
