Question

The following geometric sequences represent the populations of two bacterial cultures after 0 hours, 1 hour, 2 hours, and so on. Culture A starts with more bacteria, but culture B has a ratio of increase that is twice as large. Which culture will have the greatest population after 10 hours?

Culture A: 1000, 2000, 4000, 8000, ...
Culture B: 1, 4, 16, 64, ...

Answer 1

The formula to find the nth term of a geometric relation is \[a \times r ^{n-1}\] where a is the first term, r is the ratio of any two consecutive terms (like 2000/1000=2 and 4000/2000=2). The ratio remains constant. n is the position of the term you want, in this case 10.
Find out the 10th term for both of the cultures, i will confirm if they are right.

Answer 2

Okay thank you let me try it

Answer 3

for A I got 1,023,999

Answer 4

For B I got 1048575

Answer 5

i did not get the same answer...
did you\[r^{n-1}=2^{9}\]\[which = 512\] which is then to be multiplied with 1000
which gives 512000

Answer 6

Whoa, not at all

Answer 7

thanks though