Question

Which exponential function has the greatest average rate of change over the interval [ 0 , 2 ]

Answer 1

The exponential function which has the greatest average rate of change over the interval [0, 2] is option B.

How to calculate the average rate of change?

Mathematically, the average rate of change between two (2) points can be calculated by using this expression;

$Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}$

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.

Read more on average rate of change here: brainly.com/question/3493733

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