Challenging decreasing Geometric Sequence?

Question

"When Hillary bought the next bag of food she did so just in time.Her normally petite lizard started an amazing growth spurt eating 1.5 times as the previous day. How long will this new bag last?"
I found there are 182 pellets a bag and she was eating 6 pellets every day pre growth spurt. I got 8 days by a table but need a sequence formula and I'm not quite sure of the common ratio. Thanks in advance.

Answer 1

The common ratio is simply 1.5.

f(t) = 6 * (1.5)^t

Day 0: 6 pellets
Day 1: 9 pellets
Day 2: 13.5 pellets
Day 3: 20.25pellets
Day 4: 30.375 pellets
Day 5: 45.5625 pellets
Day 6: 68.34375 pellets

If you add it up (not counting day 0), I get that she would eat through a total of 187.03125 pellets by the end of day 6, so she runs out before the end of day 6.

Answer 2

The sum of the first n terms is [a(1) times (1 - r^n)]/[1 - r]

a(1) is 6, r is 1.5

So 6(1-1.5^n)/(1-1.5) <= 182 is the inequality

6(1 - 1.5^n)/-0.5

-12(1 - 1.5^n) <= 182

1 - 1.5^n >= 182/-12or -15 1/6

-1.5^n >= -16 1/6

1.5^n <= 16 1/6

n log 1.5 <= log 16 1/6
n <= (log 16 1/6)/log 1.5

n <= 6.7

So at most 6 days

Does that check with your table?