Question

The sequence graphed below shows the number of bicycles detailed per hour in a bicycle shop.
f(n)
n
0
4 6 8
Number of Hours
Determine the recursive formula that describes this situation.
The recursive function that describes this situation is f(1) = 4,
Number of Bicycles
20+
16-
12-
8
2
10
for n ≥ 2, and (9) =
Helpp me

Answer 1

The recursive function is f(n + 1) = 2f(n) where f(1) = 4

How to determine the recursive function?

From the graph, we have the following values

f(1) = 4

f(2) = 8

f(3) = 12

Divide f(2) by f(1) to calculate the rate (r)

r = f(2)/f(1)

r = 8/4

r= 2

Substitute r= 2 in r = f(2)/f(1)

f(2)/f(1) = 2

Make f(2) the subject

f(2) = 2f(1)

Express 2 as 1 + 1

f(1 + 1) = 2f(1)

Express 1 as n

f(n + 1) = 2f(n)

Hence, the recursive function is f(n + 1) = 2f(n) where f(1) = 4

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