For a science experiment, I planted a flower. The flower was 2 inches tall when I planted it and I observed that it grew an inch every week. 1 2 Represent this situation algebraically two ways – once using an explicit function and a second time using a recursive function. Be sure to define your variables.
1. Explicit Function:
Let's define the height of the flower as a function of the number of weeks passed. Let "h" represent the height of the flower in inches and "w" represent the number of weeks passed.
The explicit function that represents this situation can be written as:
h(w) = 2 + w
Here, the initial height of the flower is 2 inches, and for every week (represented by "w") that passes, the height increases by 1 inch.
2. Recursive Function:
A recursive function defines the height of the flower based on the previous week's height. Let "h(w)" represent the height of the flower in inches after "w" weeks.
The recursive function that represents this situation can be written as:
h(1) = 2 (Initial height when w = 1)
h(w) = h(w-1) + 1 (For every subsequent week, the height increases by 1 inch compared to the previous week)
In this case, the initial height of the flower is 2 inches (when w = 1), and for every subsequent week (w > 1), the height is determined by adding 1 inch to the previous week's height.