Question

How do you do this? Please give explanation

Answer 1

Answer:

  2, 1, 3, 4, 6, 5

Step-by-step explanation:

The rate of change of function f(x) on an interval [a, b] is defined as ...

  average rate of change = (f(b) -f(a))/(b -a)

For the function h(x) = 2^-x, this will be ...

  arc = (h(b) -h(a))/(b -a) = (2^-b -2^-a)/(b-a) = (2^-a)(2^(a-b) -1)/(b -a)

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1. For the interval [0, 2], the average rate of change is ...

  arc = (2^-0)(2^(0-2) -1)(2 -0) = (1/4 -1)/2 = -3/8 = -0.375

  1 goes in the 2nd answer blank

2-6. For the other intervals, it is convenient to let a calculator or spreadsheet compute the values. The average rates of change are shown in the attachment.