SOLUTION: can someone please help with this, I am not sure how to set the problem up, or work it. I think the answer is 8 days.. I just don't know how to work the problem.. an ant farm

Question 341875: can someone please help with this, I am not sure how to set the problem up, or work it. I think the answer is 8 days.. I just don't know how to work the problem..
an ant farm can hold 100,000 ants. If the farmheld 1500 ants on the first day, 3000 ants on the second day, 6000 ants on the third day, ad so on forming a geometric sequence, in how many days will the farm be full
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
an ant farm can hold 100,000 ants. If the farmheld 1500 ants on the first day, 3000 ants on the second day, 6000 ants on the third day, ad so on forming a geometric sequence, in how many days will the farm be full
---
The sequence: 1500,3000,6000,etc
a(1)= 1500
r = 3000/1500 = 2
----
Sum of n terms = a(1)[(r^n -1)/(r-1)]
---
You want the sum to be >= 100,000
1500[(2^n -1)/(2-1)] >= 100,000
---
2^n-1 >= 100,000/1500
2^n >= 66 2/3 + 1
2^n>= 67.67
Solve the equality:
2^n = 67.67
n(log(2)) = log(67.67)
n = [log(67.67]/[log(2)]
n = 6.0589
----
It will take a little more than 6 days to reach 100,000 ants.
It will happen in the 7th day.
===============
Cheers,
Stan H.
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