Logarithms Solve Exponential Worksheets Grade 11

1. 11^(x - 2) = 37
2. A biologist is studying bacterial growth in a lab culture. The population P(t) after t hours is modeled by the exponential function P(t) = 500 × 2^(0.3t). Determine how many hours it will take for the bacterial population to reach 8,000 organisms.
3. A radioactive substance decays according to the exponential model N(t) = N₀e^(-kt), where N₀ is the initial amount. After 24 hours, only 12.5% of the original substance remains. A scientist draws a graph showing the decay curve, with time on the horizontal axis and remaining substance percentage on the vertical axis. Determine the half-life of this substance (the time when 50% remains) using logarithmic methods.

…and 5 more problems

1. 7^(x - 3) = 42
2. A biologist is studying bacterial growth in a lab culture. The population P(t) follows the exponential model P(t) = 5000 × e^(0.03t), where t is time in hours. If the lab's containment system can only handle 15,000 bacteria safely, how many hours (to the nearest tenth) can pass before the population reaches this safety limit?
3. Isabella is monitoring the growth of a rare orchid species in a botanical garden. The height of the orchid, in centimeters, is modeled by the function H(t) = 7 × 2^(0.2t), where t is the number of weeks since Isabella began her observation. The orchid will be ready for public display when its height reaches 112 centimeters. How many weeks will it take for the orchid to reach this height? Use logarithms to solve.

…and 5 more problems

1. A pharmaceutical company is testing a new drug that decays exponentially in the bloodstream. The concentration C(t) in milligrams per liter is modeled by C(t) = 80 × 2^(-0.1t), where t is time in hours. The drug becomes ineffective when its concentration drops below 5 mg/L. How many hours will it take for the drug to reach this ineffective concentration level?
2. Dr. Chen is studying bacterial growth in her lab. She observes that a colony of bacteria doubles in size every 4 hours. If she starts with 500 bacteria, how many hours will it take for the colony to reach 32,000 bacteria? Use logarithms to solve this exponential growth problem.
3. A radioactive substance decays according to the exponential model N(t) = N₀e^(-λt), where N₀ is the initial amount. A scientist observes that after 8 years, only 25% of the original substance remains. The scientist graphs the decay function on a coordinate plane where the x-axis represents time in years and the y-axis represents the percentage of substance remaining. Determine the decay constant λ (to three decimal places) using logarithmic methods.

…and 5 more problems