Exponential Models Worksheets Grade 11

1. Isabella collected data on the cooling of a liquid: time (min) = 0, 8, 16, 24; temperature (°C) = 95, 47.5, 23.75, 11.875. Is an exponential model appropriate? Justify your answer.
2. 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.
3. A biologist is studying bacterial growth in a lab culture. The initial population is 500 bacteria, and observations show the population doubles every 3 hours. The biologist models this growth with the function P(t) = P₀ * e^(kt), where t is time in hours. Determine the value of the continuous growth rate k for this bacterial population.

…and 4 more problems

1. Sophia analyzed data: x=0, y=64; x=1, y=32; x=2, y=16; x=3, y=8. Is an exponential model appropriate?
2. 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.
3. Sophia is analyzing the growth of a certain type of algae in a controlled pond. She measures the surface area covered by the algae (in square meters) at the beginning of each day for five days. Her data is shown below: Day 0: 12 m² Day 1: 18 m² Day 2: 27 m² Day 3: 40.5 m² Day 4: 60.75 m² Determine whether the data can be modeled by an exponential function. Justify your answer by explaining the pattern in the data, and if appropriate, write an exponential function of the form A(t) = A₀ * r^t that models the area covered after t days.

…and 3 more problems

1. Emma recorded the temperature of a cooling liquid: Time (min) 0, 5, 10, 15; Temperature (°C) 80, 40, 20, 10. Is an exponential model appropriate? Justify your answer.
2. Matiu analyzed bacterial growth data: Day 0: 15, Day 1: 45, Day 2: 135, Day 3: 405. Is an exponential model appropriate? Justify your answer by calculating the ratio between consecutive y-values.
3. A research scientist is studying bacterial growth in a lab culture. The initial population is 500 bacteria, and observations show the population doubles every 3 hours. The scientist models this growth with the function P(t) = P₀ * e^(kt), where t is time in hours. Determine the value of the continuous growth rate k for this bacterial population.

…and 4 more problems