Question

Your home state uses a linear model \[y=22\left( x-70 \right)+4338\] to predict the number of vacationers $\left( y \right)$ as compared to the average temperature for that week $\left( x \right)$. Find the number of vacationers predicted for a week with an average temperature of 68 degrees?
(a) 7374 vacationers
(b) 5764 vacationers
(c) 95,362 vacationers
(d) 4294 vacationers.

Answer 1

Hint: We start solving the problem by understanding all the given information about the linear model that’s just given in the problem. We then substitute the average temperature in place of $x$ that was mention in the problem. We then make the necessary calculations to complete the problem and get the required result.

Complete step-by-step solution:
According to the problem, we have given a linear model \[y=22\left( x-70 \right)+4338\] used by home state to predict the number of vacationers $\left( y \right)$ comparing with the average temperature for that week $\left( x \right)$. We need to find the total number of vacationers for a week if the average temperature is 68 degrees.
So, we have got the value of $x$ as 68 degrees and we need to find the total number of vacationers $y$ in that week. Let us substitute the value of $x$ in the linear model \[y=22\left( x-70 \right)+4338\].
So, we have \[y=22\left( 68-70 \right)+4338\].
$\Rightarrow y=22\left( -2 \right)+4338$.
$\Rightarrow y=-44+4338$.
$\Rightarrow y=4294$.
We have predicted a total of 4294 vacationers in that week.
$\therefore$ The number of vacationers predicted for a week with an average temperature of 68 degrees is 4294 vacationers.
The correct option for the given problem is (d).

Note: We should not assume that vacationers will always increase which is not feasible every time. We should not make calculation mistakes while solving this problem. Here we have given the linear model which made us calculation easier. We can also expect models that were not linear (for e.g., exponential, cubical, etc) to predict the vacationers of that week. We can also solve such problems by just substituting the given information.