Question

A bacterium cell splits into 2 cells every hour. Write and evaluate and exponenetial expression to find how many cells there will be in 6 hours. Then use your answer to help you find the number of hours it will take for there to be 1,024 cells?..

Answer 1

There will be 64 cells in 6 hours. It will take 10 hours for there to be 1,024 cells.

Explanation:

For this question, we need to think exponents. When the cell splits, two cells arise, then 4, then 8, and so on. Each time, the count doubles, so 2 will be the base, with 6 being the exponent due to 6 hours having elapsed.

Expression:
`2^6=x\\64=x`

Using our equation will be a lot more useful for the second part of the question. We'll still use 2 as the base, but we're using x as the exponent (x represents the amount of hours it takes to reach y cells, which in this problem is 1,024):

`2^(x) =1,024\\log_(2)1,024=x\\ 10=x\\or\\2^x=2^10\\x=10`