SOLUTION: describes the book 6 A police department believes that arrest rates R are a function of the number of plainclothes officers n assigned. The arrest rate is defined as the percentage

Question 1194503: describes the book 6 A police department believes that arrest rates R are a function of the number of plainclothes officers n assigned. The arrest rate is defined as the percentage of cases in which arrests have been made. It is believed that the relationship is linear and that each additional officer assigned to the plainclothes detail results in an increase in the arrest rate of 1.20 percent. If the current plainclothes force consists of 16 officers and the arrest rate is 36 percent: (a) Define the function R=f(n). (6) Interpret the meaning of the R intercept. (c) Determine the restricted domain and range for the function. (1) Sletch the function.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
With 16 officers, one would expect 19.2 arrests, since 16*1.2 is 19.2
The actual rate is 36, so there is a 36-19.2=16.8 arrests that are built into the function without officers. That is the intercept.
R=1.2x+16.8
The intercept suggests the rate if there are no officers. Intercepts that are outside of the sensible domain are often do not makes sense.
The range is (16.8, 100), since this is per cent.
For the domain, R cannot be >100, so 100=1.2x+16.8, and x=69.3 or 69 officers
The domain is (1, 69.3) using 1 as a low bound since presumably 0 officers would not be a department.

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