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...
Situation 1: A company manufactures and sells bicycles. The number of bicycles produced each month is directly proportional to the number of employees working in the production line. As the number of employees increases, the number of bicycles produced also increases.
Situation 2: A rocket is launched into the air. Its height above the ground as a function of time does not follow a straight line. Initially, the rocket accelerates upwards rapidly, but as it reaches a higher altitude, the rate of ascent slows down. Eventually, the rocket reaches its maximum achievable height and begins to descend.
Now it's up to the classmates to determine which situation is linear and which is nonlinear.
Solution:
The linear situation is Situation 1, where the number of bicycles produced each month is directly proportional to the number of employees.
Function: Let's represent the number of bicycles produced as 'y' and the number of employees as 'x'. A linear function that models this situation could be written as y = mx + b, where 'm' represents the constant rate of production per employee and 'b' represents the baseline production when there are no employees.
One possible function that models this situation is y = 10x + 50. This means that for each additional employee, the company can produce an additional 10 bicycles. The baseline production, when there are no employees, is 50 bicycles.
Ordered pair: (5, 100)
Explanation: The ordered pair (5, 100) represents the situation where there are 5 employees in the production line, resulting in the production of 100 bicycles. This means that when there are 5 employees, the company can produce 100 bicycles in a month, considering the linear relationship between the number of employees and the number of bicycles produced.