of 25 The following geometric sequences represent the populations of two bacterial cultures at the 1-hour...

Question

Question 25 of 25
The following geometric sequences represent the populations of two bacterial cultures at the 1-hour mark, the 2-hour mark, the 3-hour mark, and so on. Culture A starts with more bacteria, but Culture B has a ratio of increase that is larger. Which culture will have the greater population at the 18-hour mark?
Culture A: 900, 1350, 2025, 3037.5, ...
Culture B: 10, 20, 40, 80, ...
A. Culture A
B. Culture B

SnapAndSolve AI · Accepted Answer

Culture A: The sequence is 900, 1350, 2025, 3037.5, ... with a common ratio of 1.5.Culture B: The sequence is 10, 20, 40, 80, ... with a common ratio of 2.To find the population at the 18-hour mark, use the formula for the nth term of a geometric sequence: a_n = a_1 * r^(n-1). Culture A: a_18 = 900 * (1.5)^17 Culture B: a_18 = 10 * (2)^17 Calculating these: Culture A: a_18 ≈ 900 * 437.89 ≈ 394,101 Culture B: a_18 = 10 * 131072 = 1,310,720 Answer: B. Culture B

contact us

Contact Info

of 25 The following geometric sequences represent the populations of two bacterial cultures at the 1-hour...

Answer

Have a similar question?

More math questions