Exponential Growth Dynamics

About this quiz

What this quiz asks

1. A bacterial colony doubles every hour. If the initial population at t=0 is 100 cells, how many cells will be present after 4 hours?
2. A wildlife population follows the model P(t) = 500 * e^(0.05t), where t is in years. Calculate the population after 20 years. (Use e ≈ 2.718)
3. An invasive species population triples every 3 months. If the current population is 50, how long will it take to reach 450 individuals?
4. A population decreases by 20% each year due to resource scarcity. Starting with 1000, what is the population after 2 years?
5. An investment of $1,000 grows at an annual interest rate of 5% compounded annually. Calculate the total balance after 2 years using the compound interest formula A = P(1 + r)^t.
6. If $5,000 is deposited into an account with a 4% annual interest rate compounded semi-annually (n=2), what is the amount after 1 year? Use A = P(1 + r/n)^(nt).
7. A sum of $2,000 is invested at 6% interest compounded continuously. Using the formula A = Pe^(rt), find the value after 3 years (e ≈ 2.718).
8. Compare two accounts: Account A ($1,000 at 5% compounded annually) and Account B ($1,000 at 4.9% compounded continuously). Which is worth more after 10 years?
9. A social media post initially reaches 50 people. If the reach triples every 2 hours, how many people will have seen the post after 6 hours?
10. A video goes viral such that the number of shares doubles every 30 minutes. If 100 people share it at t=0, what is the expression for the number of shares after t hours?
11. Information spreads in a closed network at a rate where the number of informed individuals I(t) follows I(t) = 50 * e^(0.4t). Find the rate of change of information propagation at t=5.
12. A rumor spreads such that the number of people who know it is N(t) = 1000(1 - e^(-0.2t)). As t approaches infinity, how many people know the rumor?
13. According to Moore's Law, the number of transistors on a microchip doubles approximately every 2 years. If a chip currently has 10 billion transistors, how many transistors will it have in 6 years?
14. A data storage technology follows a scaling law where its cost per gigabyte decreases by 30% every year. If the current cost is $100 per GB, what is the cost after 2 years?
15. Compute the total computing power if a system grows at a continuous rate of 20% annually. If the initial power is 100 PFLOPS, what is the power after 5 years? (Use e ≈ 2.718)
16. A neural network's parameter count grows according to N(t) = 10⁶ × 10^(t/3), where t is in years. How many years does it take for the parameter count to increase by a factor of 1000?
17. In a simplified model of a nuclear chain reaction, each fission event releases 3 neutrons, which then trigger further fissions. If the number of fissions at step n is given by N(n) = 3^n, calculate the total number of fission events occurring exactly at the 4th generation (n=4).
18. A nuclear reactor core starts with an initial population of 100 neutrons. If the neutron population increases by 50% every microsecond due to a chain reaction, determine the population after 3 microseconds using the formula P(t) = P₀(1 + r)^t.
19. In a controlled nuclear environment, the multiplication factor k is 1.05. If the initial number of fissions is 1,000, calculate the total number of fissions after 10 generations, given by F = F₀ * k^n. (Round to the nearest whole number).
20. A subcritical mass has a decay constant such that the neutron population halves every 0.5 seconds. If the initial population is 800,000, which of the following expressions correctly represent the population after 1.5 seconds?
21. A non-renewable mineral reserve is extracted at a constant rate of 2% of the remaining total each year. If the initial reserve is 1,000,000 tons, what is the remaining reserve after 5 years? (Use A = P(1-r)ᵗ)
22. An aquifer starts with 500 km³ of water. Extraction and natural seepage cause a 3.5% annual reduction. Calculate the remaining volume after 10 years. (Use A = P(1-r)ᵗ)
23. A forest carbon sink absorbs CO₂. Due to deforestation, the area shrinks by 4% annually. If the current sink capacity is 200,000 tons, what is the capacity after 15 years?
24. A rare earth metal mine has 50,000 tons. Extraction efficiency drops, but annual production is 5% of current stock. How many years until the stock is below 25,000 tons? (Solve for t: 0.5 = 0.95ᵗ)

Answer choices and explanations are shown when you take the quiz.

Topics

Quizzes on Remee

Remee quizzes come in six formats — including image questions, matching, drag-and-drop and branching — and can be played live with up to 35 people at once, which makes them work as easily in a classroom as they do on your own.