Final answer:
The explicit formula to represent the given cell growth scenario is f(n) = 1*4^n, following the form of the generic exponential growth equation f(n) = a*r^n. This formula signifies the growth of cells in a fish dividing into 4 cells every hour, resulting in an exponentially increasing sequence of cells.
Step-by-step explanation:
The cell growth described in your problem represents an example of exponential growth. Exponential growth in mathematics refers to values that increase increasingly rapidly over time due to the phenomenon of multiplication by a fixed amount in each step (in this case, after each hour). The explicit formula that represents this situation is given by the equation: f(n) = a*r^n, where 'f(n)' represents the cells after 'n' hours, 'a' is the original number of cells, 'r' is the exponential growth factor, and '^' indicates 'to the power of'.
In the context of your problem, the original number of cells 'a' is 1, and the cells multiply by 4 every hour, so 'r' would be 4. Therefore, the explicit formula to represent this cell growth scenario would be f(n) = 1*4^n.
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