A tree has 99,400 leaves before autumn. Once autumn begins, the number of leaves on a tree decreases at a rate of 13% per day. After t days of autumn, there are fewer than 12,000 leaves on the tree.

Which inequality represents this situation, and after how many days of autumn will the number of leaves on the tree be fewer than 12,000?

A. 12,000 (1.087) t > 99,400; 18 days

B. 99,400 (1.13) t > 12,000; 15 days

C. 12,000 (0.913) t < 99,400; 17 days

D. 99,400 (0.87) t < 12,000; 16 days

The answer to this question would be: D. 99,400 * (0.87) ^t < 12,000; 16 days

In this question, the initial number of leaves is 99,400 and it will decrease by 13% each day. Decrease by 13% can be put become: 100%-13%=87% of the original number.

Then, the function for the number of the leaves should be:

99,400 * (0.87) ^t

to find how many days after autumn that the tree leaves is less than 12,000 the calculation should be:

99,400 * (0.87) ^t <12,000

(0.87) ^t< 0.1207

The smallest number would be (0.87) ^16 = 0.10772290133

Its d d is the answer