This table shows values that represent an exponential function. х
0
y
1
2
1
2
4
3
8
4
5
6
16
32
64
What is the average rate of change for this function for the interval from x = 1
to x = 3?
O A. 6
OB.
O c. 1
OD. 3
SUBMIT

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Ответ:

sarah19Nursing

31.05.2020

Mathematics

$\displaystyle 25 \sqrt{6}$

Step-by-step explanation:

the triangle ∆ABD is a special right angle triangle of which we want to figure out length of its shorter leg (AB).

to do so we need to find the length of AD (the hypotenuse). With the help of ∆ADC it can be done. so recall law of sin

$\boxed{ \displaystyle \frac{ \alpha }{ \sin( \alpha ) } = \frac{ \beta }{ \sin( \beta ) } = \frac{ c}{ \sin( \gamma ) } }$

we'll ignore B/sinB as our work will be done using the first two

step-1: assign variables:

$\sin( \gamma ) = \sin( {60}^{ \circ} )$ c=AD

$\rm \sin( \alpha ) = \sin( {180}^{ \circ} - ({60}^{ \circ} + {75}^{ \circ} )) = \sin( {45}^{ \circ} )$ a=100

step-2: substitute

$\displaystyle \frac{100}{ \sin( {45}^{ \circ} )} = \frac{AD }{ \sin( {60}^{ \circ} )}$

recall unit circle therefore:

$\displaystyle \frac{100}{ \dfrac{ \sqrt{2} }{2} } = \frac{AD }{ \dfrac{ \sqrt{3} }{2} }$

simplify:

$AD = 50 \sqrt{6}$

since ∆ABD is a 30-60-90 right angle triangle of which the hypotenuse is twice as much as the shorter leg thus:

$\displaystyle AB = \frac{50 \sqrt{6} }{2}$

simplify division:

$\displaystyle AB = \boxed{25 \sqrt{6} }$

and we're done!

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This table shows values that represent an exponential function. х 0 y 1 2 1 2 4 3 8 4 5 6 16 32 64 What is the average rate of change for this function for the interval from x = 1 to x = 3? O A. 6 OB. O c. 1 OD. 3 SUBMIT