Question

Using what you have learnA 2-column table has 5 rows. The first column is labeled x with entries negative 1, 0, 1, 2, 3. The second column is labeled y with entries one-tenth, one-half, five-halves, StartFraction 25 Over 2 EndFraction, StartFraction 125 Over 2 EndFraction
What is the rate of change of the function described in the table?

Twelve-fifths
5
StartFraction 25 Over 2 EndFraction
25ed, write a generalization about government in Latin America.

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

What is the rate of change of the function described in the table?

$\displaystyle \sf{a) \: \: \frac{12}{5} }$

b) 5

$\displaystyle \sf{c) \: \: \frac{25}{2} }$

d) 25

EVALUATION

Here the given values of y are

$\displaystyle \sf{ \frac{1}{10} , \frac{1}{2} , \frac{5}{2}, \frac{25}{2} , \frac{125}{2} }$

From above we see that the values of y are in Geometric Progression

So there is an exponential relation between x and y

$\sf{Let \: \: y = b \times {a}^{x} }$

Now

$\displaystyle \sf{ \frac{1}{10} , \frac{1}{2} , \frac{5}{2}, \frac{25}{2} , \frac{125}{2} }$

$\displaystyle \sf{For \:x = - 1 \: we \: have \: y = \frac{1}{10} }$

$\displaystyle \sf{ \frac{1}{10} = b \times {a}^{ - 1} } \: \: - - (1)$

$\displaystyle \sf{For \:x = 0 \: we \: have \: y = \frac{1}{2} }$

$\displaystyle \sf{ \frac{1}{2} = b \times {a}^{ 0} } \: \: - - (2)$

From Equation 2 we get

$\displaystyle \sf{b= \frac{1}{2} }$

From Equation 1 we get

a = 5

Therefore

$\displaystyle \sf{y = \frac{ {5}^{x} }{2} }$

Hence the required rate of change = 5

FINAL ANSWER

Hence the correct option is b) 5

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Answer 2

Answer:

A

Step-by-step explanation:

i took the test on ege