Exponential Models Worksheets Grade 11

1. Kaia recorded the number of bacteria in a culture over time: (0, 81), (1, 27), (2, 9), (3, 3). Is an exponential model appropriate? Justify your answer by calculating the ratio between consecutive y-values.
2. Olivia analyzed data: x=1, y=7; x=3, y=63; x=5, y=567; x=7, y=5103. Is an exponential model appropriate? Justify by checking constant ratios.
3. Emma is monitoring the growth of a rare fungus in a controlled laboratory environment. She records the area covered by the fungus (in square centimeters) at the start of each day for five days: Day 0: 5 cm² Day 1: 15 cm² Day 2: 45 cm² Day 3: 135 cm² Day 4: 405 cm² Determine whether the growth of the fungus is best modeled by a linear function or an exponential function. Justify your answer by explaining the pattern observed in the data.

…and 4 more problems

1. Isabella recorded the number of bacteria in a culture over time: (0, 27), (1, 81), (2, 243), (3, 729). Determine if an exponential model is appropriate by calculating the ratio between consecutive y-values.
2. Mere recorded the population of bacteria in a lab experiment: Day 0: 12, Day 1: 36, Day 2: 108, Day 3: 324. Is an exponential model appropriate? Justify by calculating the ratio between consecutive y-values.
3. A biologist is studying a population of bacteria that grows exponentially. The initial population is 500 bacteria, and after 3 hours, the population reaches 4,000 bacteria. Write an exponential function in the form P(t) = P₀e^(kt) that models this growth, where t is time in hours.

…and 4 more problems

1. Sophia analyzed data from a chemical reaction experiment. The concentration of substance A was measured every 6 minutes: (0, 81), (6, 27), (12, 9), (18, 3). Is an exponential model appropriate for this data? Justify your answer by calculating ratios.
2. Mere analyzed data from a chemical reaction: time (min) = 0, 2, 4, 6; concentration (mg/L) = 64, 16, 4, 1. Is an exponential model appropriate? Justify your answer.
3. A research team is studying the spread of information through social media. They model the number of people who have seen a viral post using the function P(t) = 5000 / (1 + 49e^(-0.3t)), where t is time in hours after the post was first shared. How many people had seen the post when it was first shared (at t = 0)?

…and 3 more problems