Regression Exponential Worksheets Grade 11

1. Find the exponential regression model y = ab^x for the data points (2, 8.3), (4, 17.2), (6, 35.6), (8, 73.8), (10, 152.9). Round a and b to two decimal places.
2. An epidemiologist is tracking the spread of a new virus in a city. The number of confirmed cases was recorded over 5 days: Day 1: 85 cases, Day 2: 127 cases, Day 3: 190 cases, Day 4: 285 cases, Day 5: 428 cases. Determine the exponential regression model in the form y = ab^x that best fits this data, where x is the day number and y is the number of cases. Round coefficients a and b to three decimal places.
3. A marine biologist is studying the growth of a bacterial culture in a nutrient solution. After collecting data for 5 days, she records the following population counts: Day 1: 120 bacteria, Day 2: 180 bacteria, Day 3: 270 bacteria, Day 4: 405 bacteria, Day 5: 608 bacteria. Determine the exponential regression model in the form y = ab^x that best fits this data, where x represents the day number and y represents the bacterial population.

…and 3 more problems

1. A biologist is studying bacterial growth in a petri dish. The population doubles every 2 hours. At time t=0 hours, there are 50 bacteria. The biologist plots the data points (0, 50), (2, 100), (4, 200), and (6, 400) on a semi-log graph where the y-axis is logarithmic. Determine the exponential regression model that fits this data in the form y = ab^x.
2. Charlotte is a financial analyst tracking the quarterly revenue growth of a rapidly expanding technology startup. The company's quarterly revenues (in millions of dollars) for the first five quarters are: Quarter 1: 8.4, Quarter 2: 12.6, Quarter 3: 18.9, Quarter 4: 28.35, Quarter 5: 42.525. Determine the exponential regression model in the form y = ab^x that best fits this data, where x is the quarter number and y is the revenue in millions of dollars. Round the coefficients a and b to three decimal places.
3. Find the exponential regression model y = ab^x for the data points (1, 4.5), (2, 6.8), (3, 10.2), (4, 15.3), (5, 23.0). Round a and b to two decimal places.

…and 4 more problems

1. A scatter plot shows the cooling of a liquid over time. The temperature data points are: (0, 95), (2, 76), (4, 60.8), and (6, 48.64). When plotted on a semi-log graph with temperature on the logarithmic y-axis and time on the linear x-axis, the points form a straight line. Determine the exponential regression model in the form T(t) = a * b^t that fits this cooling data, where T is temperature in degrees Celsius and t is time in minutes.
2. A marine biologist is studying the population growth of an invasive species of jellyfish in a coastal ecosystem. After collecting data for 6 months, she records the following population counts: Month 1: 120, Month 2: 180, Month 3: 270, Month 4: 405, Month 5: 608, Month 6: 912. Determine the exponential regression model of the form y = ab^x that best fits this data, where x is the month number and y is the population. Round the coefficients a and b to three decimal places.
3. A marine biologist is studying the growth of a new coral species in a reef ecosystem. After collecting data for 6 months, she records the coral colony size: Month 1: 12 cm², Month 2: 18 cm², Month 3: 27 cm², Month 4: 40.5 cm², Month 5: 60.75 cm², Month 6: 91.125 cm². Determine the exponential regression model that best fits this growth pattern, expressing it in the form y = ab^x, where y is the coral area in cm² and x is the time in months.

…and 3 more problems