Answer:
4
Step-by-step explanation:
You are given a table of function values in which x increases by 2, and you want to know the factor by which f(x) increases when x increases by 1.
Factor
Let k represent the factor by which f(x) increases when x increases by 1. This means ...
f(2) = k·f(1)
f(3) = k·f(2) = k·(k·f(1)) = k²·f(1)
64 = k²·4
k² = 64/4 = 16
k = √16 = 4
The output value increases by a factor of 4 as the input value increases by 1.
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Additional comment
The table values would also be obtained if the factor of increase were -4. That is, f(x) = -(-4)^x would give the same table. In that case, f(x) would not be a continuous function.
