The exponential function which has the greatest average rate of change over the interval [0, 2] is option B.
<h3>How to calculate the average rate of change?</h3>Mathematically, the average rate of change between two (2) points can be calculated by using this expression;
For option A, we have:
when x = 0; when x = 2;
y = 3(1.6)^x y = 3(1.6)^x
y = 3(1.6)^0 y = 3(1.6)^2
y = 3. y = 7.68
ΔA = (7.68 - 3)/(2 -0) = 2.34.
For option B, we have:
ΔA = (9 - 4)/(2 -0) = 2.5.
For option C, the exponential function has a common ratio of 2.
ΔA = 2.
For option D, we have:
ΔA = (10 - 8)/(1 -0) = 2.
In conclusion, we can logically deduce that the exponential function which has the greatest average rate of change over the interval [0, 2] is option B i.e 2.5.
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