# A colony of bats is counted every two months. The first four counts are 1200, 1800, 2700, and 4050. If this growth rate continues, (4 points) 1. What is the recurrence relation of the bat population? (2 points) 2. How many bats are there at the 12th count? Show all work. (Hint: solve the recurrence relation above)

Friday, October 1st, 2010

### Solution:

- Recurrence relation
- Note that 1800/1200 = 1.5.
- Next, take 1.5* 1800 =2700, and that is the next population.
- Now 1.5*2700 = 4050.

- To calculate the number of bats at the 12
^{th}count, take 1200 * 1.5^{11}= 1200 *86.5 = 103,797

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