Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A factory produces widgets at a rate of 200 per hour. The production line starts with 50 widgets already made. Which function represents the total number of widgets (W) produced after 't' hours of operation?
- AW(t) = 50t + 200
- BW(t) = 200t + 50
- CW(t) = 250t
- DW(t) = 200^t + 50
Show answer & explanationAnswer & explanation
Correct answer: B. W(t) = 200t + 50
This scenario describes a linear relationship. The rate of 200 widgets per hour is the slope, and the initial 50 widgets is the y-intercept (the starting amount when t=0). So, W(t) = 200t + 50.
Why the other options are wrong
- A. This incorrectly assigns the initial amount as the rate and the rate as the initial amount.
- C. This implies a starting number of 0 widgets and a rate of 250 per hour.
- D. This represents exponential growth, not a constant production rate plus an initial amount.
Linear Function from Word Problem
Translating a real-world scenario with a constant rate of change and an initial value into a linear equation (y = mx + b).
- The 'rate' or 'per unit' value typically represents the slope (m).
- The 'initial amount', 'starting value', or 'fixed cost' typically represents the y-intercept (b).
- The variable (x or t) represents the independent quantity (e.g., hours, units).
Memory trick: Rate is the slope, start is the intercept!