The bacteria in a certain culture double every 6.3 hours. The culture has 5,500 bacteria at the start. How many bacteria will cu
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Answer:
5.7 = as an improper fraction
Step-by-step explanation:
When dividing a number by 10 the decimal moves one place to the left. When we take 57 and divide it by 10, we get 5.7
Two main facts are needed here:
1. The logarithm , regardless of the base of the logarithm, exists for
.
2. The square root exists for
.
(in both cases we're assuming real-valued functions only)
By (2) we know that exists if
, or
.
By (1), we know that exists if
, or
. But as long as the square root exists, it will always be positive, so this condition will always be met.
Ultimately, then, we only require , so the function has domain
.
To determine the range, we need to know that, in their respective domains, and
increase monotonically without bound. We also know that
at minimum, at which point the square root term vanishes, so the least value the function takes on is
. Then its range would be
.