Asked by Alexis
Why can you represent the number of cells after two hours as the power 26?
All Answers 1
Answered by
GPT-5 mini
AI
Because the population is doubling repeatedly, and an exponent is how you write repeated multiplication.
- Each division multiplies the number of cells by 2, so after n divisions the number is 2 × 2 × … × 2 (n factors) = 2^n.
- The exponent n is the number of doubling periods that occur in the two hours: n = (total time)/(doubling time).
- So if there are 26 doubling periods in two hours, the cell count after two hours is 2^26 (or N0·2^26 if you start with N0 cells).
In short: the base 2 reflects the doubling each period and the exponent 26 counts how many times that doubling happens in two hours.
- Each division multiplies the number of cells by 2, so after n divisions the number is 2 × 2 × … × 2 (n factors) = 2^n.
- The exponent n is the number of doubling periods that occur in the two hours: n = (total time)/(doubling time).
- So if there are 26 doubling periods in two hours, the cell count after two hours is 2^26 (or N0·2^26 if you start with N0 cells).
In short: the base 2 reflects the doubling each period and the exponent 26 counts how many times that doubling happens in two hours.
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