The function is changing at a rate of 5 units per value of n.
We have the following relation -
f(n + 1) = f(n) + 5
and
f(0) = 7
We have to identify the rate of change of this function - f(n)
The term y = f(n) indicates that y is expressed as a function of n, where n is a independent variable and y is a dependent variable which depends on n.
We have -
f(0) = 7
for n = 0 ↔ f(1) = f(0) + 5 = 7 + 5 = 12
for n = 1 ↔ f(2) = f(1) + 5 = 12 + 5 = 17
for n = 2 ↔ f(3) = f(2) + 5 = 17 + 5 = 22
In order to find the rate of change of function -
rate = [tex]\frac{f(n+1)-f(n)}{(n +1) -n}[/tex] , where n = 0, 1, 2, 3 ....
rate = [tex]\frac{f(1)-f(0)}{0 +1-0}[/tex] = f(1) - f(0) = 12 - 7 = 5
Hence, the function is changing at a rate of 5 units per value of n.
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