Function Fitting Worksheets Grade 11

1. The population of a certain bacterial culture grows according to the model P(t) = 1200e^(0.05t), where t is time in hours. After how many hours will the population reach 3000 bacteria? Round your answer to the nearest tenth of an hour.
2. Aroha records the following data: (1, 3), (2, 9), (3, 27), (4, 81), (5, 243). Which type of function best models this data: linear, quadratic, or exponential? Justify your answer and write the equation of the model.
3. Liam is analyzing the growth of a bacterial culture in his biology lab. The culture starts with 200 bacteria and doubles every 3 hours. He needs to model the population P(t) after t hours using an exponential function. Write the function that models the bacterial population.

…and 5 more problems

1. Mason collects data on the population of bacteria in a Petri dish over time. He records the number of bacteria (in thousands) at specific hours. The data points are: (0, 12), (1, 24), (2, 48), (3, 96), (4, 192). Plot these points on a coordinate grid (time on the x-axis, population on the y-axis) and determine which type of function (linear, quadratic, or exponential) best fits the data. Then, sketch a smooth curve through the points and estimate the population at 5 hours.
2. Kaia is studying the cooling of a freshly baked loaf of bread. She records the temperature of the bread (in degrees Celsius) at various times (in minutes) after removing it from the oven. The data is shown in the table below: Time (min): 0, 10, 20, 30, 40, 50 Temperature (°C): 180, 90, 45, 22.5, 11.25, 5.625 Plot these points on a coordinate plane (time on the horizontal axis, temperature on the vertical axis). Determine which type of function (linear, quadratic, or exponential) best fits this data. Then, estimate the temperature of the bread after 60 minutes based on the pattern you observe.
3. Hana records the following data: (0, 2), (1, 6), (2, 18), (3, 54), (4, 162). Determine which function type (linear, quadratic, or exponential) best fits the data, and write the equation of the model in the form y = a * b^x or y = ax^2 + bx + c or y = mx + b.

…and 3 more problems

1. Aroha records the following data: (1, 3), (2, 9), (3, 27), (4, 81), (5, 243). Determine which type of function (linear, quadratic, or exponential) best fits this data and write the equation of the function.
2. Ava records the following data: (1, 6), (2, 11), (3, 16), (4, 21), (5, 26). Which type of function (linear, quadratic, or exponential) best fits this data? Estimate the value of the function at x = 6.
3. Noah is monitoring the growth of a certain species of bamboo over several weeks. He records the height (in centimeters) of a stalk at the end of each week: Week 1: 12 cm, Week 2: 24 cm, Week 3: 48 cm, Week 4: 96 cm, Week 5: 192 cm. Based on this pattern, determine which type of function (linear, quadratic, or exponential) best models the data, and then use that model to estimate the height of the bamboo at the end of Week 7.

…and 4 more problems