Exponential Equations and Functions
This is the amount of time it takes for the value in an exponential decay model to halve.
What is the half-life?
This is the base of a natural logarithm.
What is e?
This is whether the sequence -3, 2, 7, 12, 17, ... is arithmetic or geometric and its common difference or common ratio.
What is arithmetic with d = 5?
This is whether the geometric series 20 + 24 + 28.8 + 34.56 + ... converges or diverges.
What is since r = 1.2, the series diverges?
This Athenian philosopher believed in knowledge through dialogue rather than spoken words and in questioning to uncover deeper meaning.
Who is Socrates?
If the amount of population of a bacteria in an ecosystem effectively triples each hour continuously, starting with a single bacterium, how much bacteria will be in the ecosystem after seven and a half hours?
What is about 3,788 bacteria?
This is the value of x if 2 ln(x) + 3 = 7.
What is x = e2 ?
Or
What is x ≈ 7.39?
This is whether the sequence -100, 50, -25, 12.5, ... is arithmetic or geometric and its common difference or common ratio.
What is geometric with r = -1/2?
If it exists, this is the sum of the infinite geometric series 5 + 4 + 3.2 + 2.56 + ...
What is S = 25?
This television show holds the record as the longest prime-time drama series.
What is Law & Order: Special Victims Unit?
If the amount of a substance decays at a rate diminishing to 2/5 of its size over the course of each year, then this its half-life.
What is about 1.32 years?
This is the value of x if ln(3x - 17) - ln(2) = ln(x-1).
What is x = 15?
This is the 6th term of the arithmetic sequence with
a9 = 120 and a14 = 195.
What is a6 = 75?
This is the value of S7 for the geometric series 3 - 6 + 12 - 24 + ...
What is S7 = 129?
This is 25 mph in meters per second.
What is 11.176 m/s?
If the amount of a bacteria in a population is increasing continuously by a factor of 3.5 per hour, starting with 15 bacteria, how many minutes will it take for the population to reach 4,000 bacteria?
What is about 267.5 minuts?
OR
What is about 268 minutes?
This is the value of x if 2 log(x) - log(2x) = 5.
What is 200,000?
This is the value of the 10th term of the geometric sequence with a5 = 96 and a7 = 384.
What is a10 = 3072?
This is the only arithmetic sequence with a series that does not diverge.
What is an = 0?
Or
What is 0, 0, 0, ... ?
This is the acceleration due to gravity on Mars.
What is about 3.7 m/s² ?
Or
What is about 12.2 ft/s² ?
If the concentration of 500 ml of a medication has a half-life of 4 hours, how many minutes will it take to diminish to a concentration of 10 ml in the bloodstream?
What is about 1,354.5 minutes?
Or
What is about 1,355 minutes?
This is the value of x if 4 log(x) + 2 log(2x) = 3 log(2).
What is x = 3√2?
Or
What is x ≈ 1.26?
This is how long it will take for a principal of $10,000, compounded monthly with a 1.5% annual interest rate, to reach a balance of $11,000.
What is about 6.36 years?
If the second term of a geometric sequence is 5/54 and the fifth term of it is 625/11,664, this is the value of the sequence's infinite series.
What is S = 2/3?
This is the only Pokémon that has a base stat total equal to its National Pokédex number.
What is Archeops (#567)?