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3 years ago

11

Can someone help me please ?

2 answers:

Taya2010 [7]3 years ago

5 0

-W24 I think that is the ans2er

Triss [41]3 years ago

5 0

As you know w^8/w^2 = w4
Now
(w^4)^-6
= w^-24
= 1/w^24

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Given

Interval: (0,3)

See attachment for functions f(x), g(x) and h(x)

Required

Order from fastest to slowest decreasing average rate of change

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$Rate = \frac{f(b) - f(a)}{b - a}$

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$(a,b) = (0,3)$

i.e.

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$Rate = \frac{f(b) - f(a)}{b - a}$

$Rate = \frac{f(3) - f(0)}{3 - 0}$

$Rate = \frac{f(3) - f(0)}{3}$

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$f(x) = 16(\frac{1}{2})^x$

$f(3) = 16(\frac{1}{2})^3 = 16 * \frac{1}{8} = 2$

$f(0) = 16(\frac{1}{2})^0 = 16 * 1 = 16$

So:

$Rate = \frac{f(3) - f(0)}{3}$

$Rate = \frac{2 - 16}{3}$

$Rate = -\frac{14}{3}$

For g(x)

$Rate = \frac{g(b) - g(a)}{b - a}$

$Rate = \frac{g(3) - g(0)}{3 - 0}$

$Rate = \frac{g(3) - g(0)}{3}$

From the table of g(x)

$g(3) = 1$

$g(1) = 27$

So:

$Rate = \frac{1 - 27}{3}$

$Rate = -\frac{26}{3}$

For h(x)

$Rate = \frac{h(b) - h(a)}{b - a}$

$Rate = \frac{h(3) - h(0)}{3 - 0}$

$Rate = \frac{h(3) - h(0)}{3}$

From the graph of h(x)

$h(3) = -3$

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So:

$Rate = \frac{-3 - 4}{3}$

$Rate = -\frac{7}{3}$

So, the calculated rates of change are:

$f(x) = -\frac{14}{3}$ $= -4.67$

$g(x) = -\frac{26}{3}$ $=-8.67$

$h(x) = -\frac{7}{3}$ $=-2.33$

By comparison:

From the fastest decreasing to slowest, the order is: <em>g(x), f(x) and h(x)</em>

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3 years ago