9514 1404 393
Answer:
2^6 = 64
Explanation:
Each hour the initial value (1) is multiplied by 2 (again). So the number of times 2 multiplies the initial value is the number of passing hours (t).
The number of cells after t hours is ...
c(t) = 1×2^t = 2^t
After 6 hours, this is
c(6) = 2^6 = 64 . . . . cells after 6 hours
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Additional comment
As you know, multiplication simplifies repeated addition.
x + x + x = 3x
In a similar way, exponentiation simplifies repeated multiplication.
x·x·x = x³ . . . . (written as x^3 in plain text)
In this problem, we're repeatedly multiplying by 2. After we do that t times, the initial value is multiplied by 2^t.