Exponential Growth and Decay Worksheets Grade 10

1. Emma is studying the population growth of a rare species of orchid in a protected forest reserve. The current population is 125 orchids, and the population is expected to grow at a rate of 7% per year. Using the exponential growth model P(t) = P₀ × (1 + r)^t, where P₀ is the initial population, r is the growth rate as a decimal, and t is time in years, determine the orchid population after 9 years. Round your answer to the nearest whole number.
2. 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?
3. A population of 800 bacteria grows at a rate of 12% per hour. Write an exponential function P(t) to model the population after t hours. Then, determine the population after 5 hours, rounded to the nearest whole number.

…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. A sample of a radioactive isotope has an initial mass of 96 grams. Its half-life is 9 years. Write an exponential decay model A(t) for the mass remaining after t years, and use it to find the mass remaining after 27 years.
3. A right circular cone has a height of 12 cm and a base radius of 5 cm. The cone is intersected by a plane parallel to its base, creating a smaller cone at the top with height 4 cm. What is the volume of the frustum (the remaining portion after removing the smaller top cone)?

…and 4 more problems

1. A rare species of orchid is being cultivated in a botanical garden. The number of orchids follows the exponential growth model N(t) = 80 × 2^(t/3), where t is the time in years. How many orchids will there be after 9 years?
2. Mason invests $15,000 in a savings account that earns 8.4% annual interest compounded monthly. Write the exponential function A(t) that models the amount in the account after t years, and then determine the amount after 9 years, rounded to the nearest dollar.
3. Aroha is monitoring the growth of a rare fern species in a conservation reserve. The initial population of ferns is 135, and the population grows at a rate of 7% per year. Using the exponential growth model P(t) = P₀(1 + r)^t, where P₀ is the initial population, r is the annual growth rate as a decimal, and t is time in years, determine the population of ferns after 9 years. Round your answer to the nearest whole number.

…and 4 more problems