Situation 1:
A student is studying for a test and their score increases every hour they study. For example, after studying for 1 hour, they score 75. After studying for 2 hours, they score 85. After studying for 3 hours, they score 95. This pattern continues consistently.
Situation 2:
A plant is growing in a garden. Initially, the growth of the plant is slow. However, as time goes on, the plant starts growing faster and faster. For example, after 1 week, the plant has grown 2 inches. After 2 weeks, the plant has grown 6 inches. After 3 weeks, the plant has grown 12 inches. The rate of growth increases irregularly over time.
In the linear situation, the function that models the pattern can be written as y = mx + c, where x represents the number of hours studied and y represents the corresponding score. To find the values of m and c, we can select two points from the given examples and solve for the variables.
For example, using the points (1, 75) and (2, 85):
Using the point-slope form, m = (85 - 75) / (2 - 1) = 10
Using the slope-intercept form, c = 75 - 10(1) = 65
Therefore, the linear function that models the situation is y = 10x + 65.
One ordered pair that would be a solution to this linear function, for example, is (4, 105). This means that after studying for 4 hours, the student is expected to score 105.
In the context of the situation, the ordered pair (4, 105) represents the score the student is predicted to achieve after studying for 4 hours.
Describe a situation that models a linear pattern and then describe a situation that models a nonlinear pattern. Do not state which situation is linear and which is nonlinear. Your classmates will need to determine which is which and then write a function that models the linear situation. Your classmates will also need to write 1 ordered pair that is a solution to the linear function and explain its meaning in the context of the situation.
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