Function Fitting Worksheets Grade 11

1. Emma is monitoring the height of a sunflower plant over several days. She records the following data: Day 0: 15 cm, Day 5: 30 cm, Day 10: 60 cm, Day 15: 120 cm, Day 20: 240 cm. Determine which type of function (linear, quadratic, or exponential) best models the height of the sunflower over time. Explain your reasoning and write the function that fits the data.
2. A scientist records the following data for a population of bacteria over time (hours): (0, 50), (1, 100), (2, 200), (3, 400), (4, 800). Determine which function type (linear, quadratic, or exponential) best fits the data, and estimate the population at t = 5 hours.
3. Noah is studying the spread of a new plant species in a forest. He records the area covered by the plants (in square meters) at different times (in years since the first observation). The data is: t (years): 1, 2, 3, 4, 5 A(t) (m²): 6, 16, 36, 66, 106 Determine which type of function (linear, quadratic, or exponential) best models the data, and estimate the area covered after 6 years.

…and 5 more problems

1. Emma is studying the cooling of a cup of coffee in her physics class. She measures the temperature of the coffee every 10 minutes and records the following data: at t = 0 min, temperature = 95°C; at t = 10 min, temperature = 71°C; at t = 20 min, temperature = 55°C; at t = 30 min, temperature = 44°C. The room temperature is constant at 21°C. Determine which type of function (linear, quadratic, or exponential) best models the temperature difference (coffee temperature minus room temperature) over time, and write the specific function that fits the data for the temperature difference as a function of time in minutes.
2. Noah records the following data: (1, 12), (2, 36), (3, 108), (4, 324), (5, 972). Determine which function type (linear, quadratic, or exponential) best fits the data, and write an approximate equation for the function.
3. Tane records the following data: (1, 5), (2, 15), (3, 45), (4, 135), (5, 405). Which type of function (linear, quadratic, or exponential) best models this data? Sketch a curve through the points and estimate the value when x = 6.

…and 4 more problems

1. Ava is studying the cooling of a liquid in a chemistry lab. She records the temperature of the liquid every 10 minutes and obtains the following data: at t = 0 minutes, temperature = 96°C; at t = 10 minutes, temperature = 76°C; at t = 20 minutes, temperature = 61°C; at t = 30 minutes, temperature = 51°C; at t = 40 minutes, temperature = 46°C; at t = 50 minutes, temperature = 43°C. Which type of function (linear, quadratic, or exponential) best models this cooling data, and what is the approximate temperature at t = 60 minutes based on that model?
2. Tane records the following data: (1, 12), (2, 36), (3, 108), (4, 324), (5, 972). Which type of function (linear, quadratic, or exponential) best fits this data? Estimate the value of the function at x = 6 using the identified model.
3. Emma records the following data: (1, 7), (2, 21), (3, 63), (4, 189), (5, 567). Determine which function type (linear, quadratic, or exponential) best fits the data, and estimate the value when x = 6.

…and 4 more problems