Exponential Growth and Decay Worksheets Grade 10

1. A population of bacteria starts at 450 and triples every 4 hours. Write an exponential function P(t) to model the population after t hours. Then, determine the population after 12 hours.
2. Hana is monitoring the decay of a radioactive isotope in a laboratory. A graph shows the mass of the isotope over time, with the mass decreasing exponentially. At time t = 0 hours, the mass is 240 grams. After 16 hours, the mass has decayed to 60 grams. The graph passes through the points (0, 240) and (16, 60). What is the half-life of the isotope in hours?
3. Aroha is observing a rare plant species in a protected forest. The population of the plants, P(t), is modeled by the exponential decay function P(t) = 8500(0.91)^t, where t is the number of years since the study began. The graph of this function shows a steep decline that gradually levels off. What is the annual percentage rate of decay of the plant population?

…and 3 more problems

1. Emma is studying a population of bacteria in a Petri dish. At 10:00 AM, she observes 500 bacteria. By 2:00 PM, the population has grown to 8000 bacteria. The growth is exponential and follows the model P(t) = P₀ · b^t, where t is the number of hours after 10:00 AM. What is the value of the growth factor b (rounded to two decimal places)?
2. Matiu invests $4,200 in a savings account that earns 8% annual interest compounded quarterly. Write the exponential function A(t) that models the amount in the account after t years, and determine the amount after 6 years, rounded to the nearest dollar.
3. Tane is a conservation biologist studying a population of rare native birds on a remote island. The initial population is 375 birds. The population is decreasing at a rate of 7% per year due to habitat loss. Write an exponential decay function P(t) to model the population after t years, and then use it to determine the number of birds remaining after 9 years. Round your answer to the nearest whole bird.

…and 3 more problems

1. A scientist, Emma, is modeling the radioactive decay of a sample of bismuth-210. The initial mass of the sample is 80 mg, and the half-life of bismuth-210 is 5 days. On a coordinate grid, Emma plots the exponential decay curve showing the mass remaining over time in days. What is the mass of the sample remaining after 15 days?
2. Liam is studying the decay of a radioactive isotope. He has a 200-gram sample, and after 9 days, only 25 grams remain. The decay follows an exponential model A(t) = A₀ * b^t, where t is time in days. What is the half-life of the isotope in days? (Round to the nearest whole number.)
3. Mere is analyzing the exponential growth of a bacterial colony in a petri dish. At 2:00 PM, she observes the colony covering an area of 4 square millimeters. At 4:00 PM, she observes the colony covering an area of 16 square millimeters. Assuming the area grows exponentially with respect to time, and using an exponential model of the form A(t) = a * b^t, where t is the number of hours after 2:00 PM, what is the area of the colony at 6:00 PM?

…and 4 more problems