Mathematics, 28.01.2020 07:31 j015

Write an exponential function y = abx for a graph that includes (–4, 72) and (–2, 18).

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Answer from: ferny5106

$y=4.5(0.5)^{x}$

Step-by-step explanation:

* Lets revise the meaning of exponential function

- The form of the exponential function is $y=ab^{x}$ ,

where a ≠ 0, b > 0 , b ≠ 1, and x is any real number

- It has a constant base b

- It has a variable exponent x

- To solve an exponential equation, take the log or ln of both sides,

and solve for the variable

* Lets solve the problem

∵ y = a(b)^x is an exponential function

∵ Its graph contains the point (-4 , 72) and (-2 , 18)

- Lets substitute x and y by the coordinates of these points

# Point (-4 , 72)

∵ $y=ab^{x}$

∵ x = -4 and y = 72

∴ $72=ab^{-4}$

- The change any power from -ve to +ve reciprocal the base of

the power ( $p^{-n}=\frac{1}{p^{n}}$

∴ $72=\frac{a}{b^{4}}$

- By using cross multiplication

∴ $a=72b^{4}$ ⇒ (1)

# Point (-2 , 18)

∵ x = -2 and y = 18

∴ $18=ab^{-2}$

∴ $18=\frac{a}{b^{2}}$

- By using cross multiplication

∴ a = 18b² ⇒ (2)

- Equate the two equations (1) and (2)

∴ $72b^{4}=18b^{2}$

- Divide both sides by 18b²

∵ $\frac{72b^{4}}{18b^{2}}=4b^{4-2}=4b^{2}$

∵ $\frac{18b^{2}}{18b^{2}}=(1)b^{2-2}=(1)b^{0}=(1)(1)=1$

∴ 4b² = 1 ⇒ divide both sides by 4

∴ $b^{2}=\frac{1}{4}=0.25$ ⇒ take square root for both sides

∴ b = √0.25 = 0.5

- Lets substitute the value ob b in equation (1) or (2) to find a

∵ a = 18b²

∵ b² = 0.25

∴ a = 18(0.25) = 4.5

- Lets substitute the values of a and b in the equation $y=ab^{x}$

∴ $y=4.5(0.5)^{x}$

- We can write it using fraction

∴ $y=\frac{9}{2}(\frac{1}{2})^{x}$

Answer from: yfnal3x

ANSWER

$y = \frac{9}{2} ( { \frac{1}{2} })^{x}$

EXPLANATION

Let the exponential function be

$y = a {b}^{x}$

Since the graph includes (–4, 72), it must satisfy this equation.

$72= a { b}^{ - 4}$

Multiply both sides by b⁴ .

This implies that,

$a = 72 {b}^{4} ...1$

The graph also includes (-2,18).

We substitute this point also to get:

$18=a {b}^{ - 2}$

Multiply both sides by b²

$a = 18 {b}^{2} ...(2)$

We equate (1) and (2) to obtain:

$72 {b}^{4} = 18 {b}^{2}$

Multiply both sides by

$\frac{72 {b}^{4} }{ {18b}^{4} } = \frac{18 {b}^{2} }{18 {b}^{4} }$

$4 = \frac{1}{ {b}^{2} }$

${2}^{ 2} = ( \frac{1}{b} )^{2}$

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

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

Put b=½ into equation (2).

$a = 18 {( \frac{1}{2} })^{2}$

$a = \frac{18}{4}$

$a = \frac{9}{2}$

Therefore the equation is

$y = \frac{9}{2} ( { \frac{1}{2} })^{x}$

Answer from: Quest

idk

step-by-step explanation:

maybe try if it is work from a book, if not try

Answer from: Quest

the first question mark is 6 and the second question mark is 26 (the square root)

step-by-step explanation:

Multiply. what is the product (3 * 10°) * (2 x 10") in scientificnotation? plzzz noww

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Write an exponential function y = abx for a graph that includes (–4, 72) and (–2, 18)....

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Mathematics, 17.10.2020 14:01

I don't know what the question is asking- I could probably figure out the equations but idk what it means