Question

researchers identified college students who generally were procrastinators or non - procrastinators. in a study, the students were asked to report throughout the semester how many symptoms of physical illness they had experienced. the study shown that late in the semester, procrastinating students reported more symptoms of physical illness than their non - procrastinating peers. complete parts (a) through (c) below.
a. at the beginning of the semester, procrastinators reported an average of 0.4 symptoms, increasing at a rate of 0.65 symptoms per week. write a function that models the average number of symptoms, y, after x weeks.
(use integers or decimals for any numbers in the equation.)

Explanation:

Step1: Identify the type of function

This is a linear function problem since the number of symptoms increases at a constant rate per week. The general form of a linear function is \( y = mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y - intercept (initial value).

Step2: Determine the values of m and b

• The initial number of symptoms (when \( x = 0 \), at the beginning of the semester) is \( b=0.4 \). This is the y - intercept.
• The rate of increase of symptoms per week is \( m = 0.65 \). This is the slope of the line.

Step3: Write the function

Substitute \( m = 0.65 \) and \( b = 0.4 \) into the linear function formula \( y=mx + b \). We get \( y=0.65x + 0.4 \).

Answer:

\( y = 0.65x+0.4 \)