Answer:
1) 2^9 = 512
2) 2^(3t) = 2^6 for t=2
Step-by-step explanation:
1) An exponent is used to signify repeated multiplication. Here, the factor 2 is repeated 9 times, so the expression can be written using an exponent as ...
2^9
Using any of a variety of means, the value of this expression can be found to be ...
2^9 = 512
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2) Assuming the bacteria reproduce by multiplying by some factor in a given time, we can divide the original expression into 3 parts:
(2×2×2) × (2×2×2) × (2×2×2)
If this represents the number after 3 hours, then the number after 2 hours is expected to be ...
(2×2×2) × (2×2×2) = 2^6
That is, there will be (2 h)/(3 h) = 2/3 times as many multiplications by a factor of 2. (2/3)(9) = 6 will be the exponent for the number after 2 hours.
