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4 years ago

Write an exponential function for graph that passes through the following points (-3,80);(-1,20)

Mathematics

1 answer:

padilas [110]4 years ago

7 0

Answer:

(

)

Explanation:

An exponential function is in the general form

(

)

We know the points

(

−

)

and

(

)

, so the following are true:

(

−

)

(

)

Multiply both sides of the first equation by

to find that

Plug this into the second equation and solve for

(

)

Two equations seem to be possible here. Plug both values of

into the either equation to find

. I'll use the second equation for simpler algebra.

(

)

Giving us the equation:

(

)

−

(

−

)

−

Giving us the equation:

−

(

−

)

However! In an exponential function,

, otherwise many issues arise when trying to graph the function.

The only valid function is

(

)

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(01.02 HC)

Phoenix [80]

By applying radical, power and rational properties we have the following results after simplifying expressions:

$x^{\frac{3}{4} }$
x
$x^{\frac{11}{10} }$
x

<h3>How to reduce radical and rational expressions into a single power expression with rational exponent</h3>

In this question we need to simplify four given expressions by using the following radical and power properties:

$\sqrt[n]{x} = x^{\frac{1}{n} }$ (1)
$x^{m+n} = x^{m}\cdot x^{n}$ (2)
$x^{m-n} = \frac{x^{m}}{x^{n}}$ (3)
$(x^{m})^{n} = x^{m\cdot n}$ (4)

Now we proceed to simplify each of the four expressions:

$\sqrt[4]{x^{3}} = x^{3/4}$
$\frac{1}{x^{-1}} = (x^{-1})^{-1} = x$
$\sqrt[10]{x^{5}\cdot x^{4}\cdot x^{2}} = \sqrt[10]{x^{11}} = x^{\frac{11}{10} }$
$x^{\frac{1}{3} }\cdot x^{\frac{1}{3} }\cdot x^{\frac{1}{3} } = x$

To learn more on power functions: brainly.com/question/18719083

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3 0

3 years ago

What is the sign of the product (–5)(–3)(–8)(–6)?

Likurg_2 [28]

The correct answer is B

$EXPLANATION$

Let us do the first product,

We have;

$(-5)\times (-3)$

We can re-group the sign and the numbers to obtain;

$(-\times -)(5\times 3)$

But we know that; negative times negative is positive. So the product becomes,

$+(5\times 3)$

Similarly for the second product,

We have;

$(-8)\times (-6)$

We can again re-group the sign and the numbers to obtain;

$(-\times -)(8\times 6)$

But we know that; negative times negative is positive. So the product becomes,

$+(8\times 6)$

Putting all together gives,

$+(5\times 3) \times +(8\times 6)$

Finally, positive times positive will also give positive. That is,

$+(5 \times 3)(8 \times 6)$