Infinite Geometric Series Worksheets Grade 12

1. A wildlife biologist is studying the spread of a conservation message through a community. Each person who hears the message shares it with exactly 0.3 new people on average. If the initial outreach reached 800 people, what is the total number of people who will eventually hear this conservation message?
2. Dr. Rodriguez is studying a new antidepressant medication that builds up in a patient's system over time. Each daily dose adds 80 mg to the bloodstream, but the body metabolizes 25% of the drug present each day. If a patient starts treatment and continues taking the medication indefinitely, what total drug concentration will approach in their system in the long run?
3. ∑(n=1 to ∞) 9(0.8)^(n-1) = ?

…and 4 more problems

1. A wildlife biologist is studying the spread of a rare bird species through a forest ecosystem. Each breeding pair successfully establishes a new nesting territory with a probability of 0.3, and these new territories then become sources for further expansion. If the initial population consists of 80 breeding pairs, what is the theoretical maximum total number of breeding pairs that could eventually be supported in this forest under ideal conditions?
2. Tane is studying the population dynamics of an endangered tree fern species in a regenerating forest. He observes that each year, the number of new fronds produced by the population is exactly one-third of the number of fronds produced in the previous year. If the fern population produced 81 new fronds in the first year of his study, and this pattern of decline continues indefinitely, what is the total number of fronds that will ever be produced by this population from the first year onward?
3. Emma is investigating the long-term accumulation of a new eco-friendly cleaning agent in a lake. Each month, a factory releases 500 kilograms of the agent into the lake. The lake's natural filtration system removes 40% of the agent present at the beginning of each month. If the factory continues this monthly release indefinitely, what total mass of the cleaning agent will accumulate in the lake in the long run?

…and 4 more problems

1. A city is planning a new public transportation system where each new train line connects to existing lines, creating a geometric growth pattern. The first line serves 12,000 daily commuters. Each subsequent line serves 75% of the previous line's ridership. If the city builds lines indefinitely following this pattern, what is the total number of daily commuters the entire system will eventually serve?
2. ∑(n=1 to ∞) 18(0.6)^(n-1) = ?
3. ∑(n=1 to ∞) 17(0.7)^(n-1) = ?

…and 4 more problems