For a science experiment, I planted a flower. The flower was 2 inches tall when I planted it and I observed that it grew 1/2 an inch every week.
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.
Explicit function:
Let h represent the height of the flower (in inches) and w represent the number of weeks since the flower was planted. The explicit function for the height of the flower can be represented as:
h = 2 + (1/2)w
Recursive function:
Let hₙ represent the height of the flower (in inches) after n weeks. The recursive function for the height of the flower can be represented as:
h₁ = 2
hₙ₊₁ = hₙ + (1/2) for n > 1