Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 785. Find a linear function, S(t), which fits this data,
And which expresses score as a function of time. Use this function to predict an average score for persons taking
A 56-hour review course. Round your answer to the tenths place.
A) 727.3
B) 720.0
C) 731.5
D) 741.3

Question

Quizplus · Accepted Answer

To find a linear function $S(t)$ that fits the given data, we can use the two points provided: $(30, 620)$ and $(70, 785)$. The linear function can be represented as $S(t) = mt + b$, where $m$ is the slope and $b$ is the y-intercept.First, we calculate the slope $m$:$$m = \frac{785 - 620}{70 - 30} = \frac{165}{40} = 4.125$$Next, we find the y-intercept $b$ by using one of the points. Let's use $(30, 620)$:$$620 = 4.125(30) + b$$$$b = 620 - 123.75 = 496.25$$Therefore, the linear function is $S(t) = 4.125t + 496.25$.To predict the average score for a 56-hour review course, we substitute $t = 56$ into the function:$$S(56) = 4.125(56) + 496.25 = 231 + 496.25 = 727.25$$Rounded to the tenths place, the predicted average score is 727.3.

Persons Taking a 30-Hour Review Course to Prepare for a Standardized