Questions: At the beginning of the semester, procrastinators reported an average of 0.8 symptoms, increasing at a rate of 0.45 symptoms per week. Choose the function that models the average number of symptoms, y, after x weeks.

At the beginning of the semester, procrastinators reported an average of 0.8 symptoms, increasing at a rate of 0.45 symptoms per week. Choose the function that models the average number of symptoms, y, after x weeks.

Transcript text: At the beginning of the semester, procrastinators reported an average of 0.8 symptoms, increasing at a rate of 0.45 symptoms per week. Choose the function that models the average number of symptoms, y, after x weeks.

Solution

Solution Steps

To model the average number of symptoms, we need to create a linear function where the initial number of symptoms is 0.8 and the rate of increase is 0.45 symptoms per week. The function will be in the form of \( y = mx + b \), where \( m \) is the rate of increase and \( b \) is the initial number of symptoms.

Step 1: Define the Function

The average number of symptoms \( y \) after \( x \) weeks can be modeled by the linear function: \[ y = 0.45x + 0.8 \] where \( 0.45 \) is the rate of increase in symptoms per week and \( 0.8 \) is the initial number of symptoms.

Step 2: Calculate Symptoms After 5 Weeks

To find the average number of symptoms after \( x = 5 \) weeks, we substitute \( x \) into the function: \[ y = 0.45(5) + 0.8 \] Calculating this gives: \[ y = 2.25 + 0.8 = 3.05 \]