Model Comparison Worksheets Grade 11

1. A right triangle is drawn on a coordinate plane with vertices at (0,0), (4,0), and (4,3). A circle is inscribed in this triangle, tangent to all three sides. What is the radius of this inscribed circle?
2. Emma is a data analyst comparing three different models for the spread of a virus in a small town. Model L predicts the number of infected people grows linearly: I(t) = 1500 + 120t, where t is days after the first case. Model Q predicts quadratic growth: I(t) = 5t² + 1500. Model E predicts exponential growth: I(t) = 1500(1.08)^t. After 15 days, which model predicts the highest number of infected people?
3. Dr. Chen is studying bacterial growth in her lab. She observes that a colony starts with 200 bacteria and doubles every 3 hours. Meanwhile, a chemical reaction she is monitoring produces heat according to the quadratic model H(t) = 2t² + 10, where H is heat in joules and t is time in hours. If she needs to find when the number of bacteria equals the heat output in joules, which type of equation must she solve and what is the general form of this equation?

…and 4 more problems

1. Isabella is a materials scientist comparing the performance of three different cooling systems for an industrial reactor. System L (linear) reduces temperature at a constant rate: T(t) = 327 - 17t, where T is temperature in degrees Celsius and t is time in minutes. System Q (quadratic) follows the model: T(t) = 327 - 2t². System E (exponential) follows the model: T(t) = 327(0.92)^t. After 12 minutes, which system will have reduced the temperature the most?
2. Mere is comparing three functions: f(x) = 6x + 4 (linear), g(x) = 2x² + 8 (quadratic), and h(x) = 4^x (exponential). For large x, which function grows fastest?
3. Aroha is comparing three functions: f(x) = 9x + 5 (linear), g(x) = 3x² + 7 (quadratic), and h(x) = 3^x (exponential). For large values of x, which function grows the fastest?

…and 5 more problems

1. Compare f(x)=11x+6, g(x)=x²+16, h(x)=6^x for large x. Which function grows fastest?
2. Hana is a city planner evaluating three models for the growth of a new urban district's population over time, where t is measured in years since the district opened. Model L predicts linear growth: P(t) = 2400 + 180t. Model Q predicts quadratic growth: P(t) = 12t^2 + 2400. Model E predicts exponential growth: P(t) = 2400(1.06)^t. Determine which model predicts the highest population after 20 years, and by how many people that model exceeds the second-highest prediction.
3. Compare f(x) = 13x + 20, g(x) = 3x² + 11, h(x) = 4^x for large x. Which function grows fastest?

…and 5 more problems