Final answer:
To determine the number of cookies Grandma originally baked, double the 2 remaining cookies for each of the 27 half-lives that have passed, resulting in 2 * 2^27 cookies.
Step-by-step explanation:
The question involves calculating the initial amount of cookies using the concept of a half-life, which is a term commonly used in mathematics and science to describe how quickly a substance decays or reduces to half its initial amount.
Solution
The half-life of Grandma's cookies is given as 2 hours. After 2 days and 6 hours (which total 54 hours), there are 2 cookies left. To find the original number of cookies, we must work backwards, doubling the remaining cookies for each half-life period.
- Total time passed: 54 hours
- Number of half-lives passed: 54 hours / 2 hours per half-life = 27 half-lives
Starting with the 2 remaining cookies, we double them 27 times:
Initial cookies = 2 * 227
By calculating 2 raised to the power of 27 and multiplying it by 2, we can find the number of cookies Grandma originally baked.