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3 years ago

Find the Exponential Regression using the table. Write the initial amount, common ratio, and equation for the table.

Mathematics

1 answer:

ikadub [295]3 years ago

6 0

Answer:

a = 5

b = 1.3863

equation;

$h(x)=5e^{1.3863x}$

Step-by-step explanation:

In this scenario, x represents the independent variable while h(x) represents the dependent variable y.

The analysis is performed in Ms. Excel. The first step is to obtain a scatter plot of the data then finally inserting an exponential trend line to obtain the required equation.

The Ms. Excel output is shown in the attachment below. To obtain the value of a we substitute x = 0 in the equation. On the other hand, the value of b is the exponent in the equation.

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Sketch the domain D bounded by y = x^2, y = (1/2)x^2, and y=6x. Use a change of variables with the map x = uv, y = u^2 (for u ?

cluponka [151]

Under the given transformation, the Jacobian and its determinant are

$\begin{cases}x=uv\\y=u^2\end{cases}\implies J=\begin{bmatrix}v&u\\2u&0\end{bmatrix}\implies|\det J|=2u^2$

so that

$\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\iint_{D'}\frac{2u^2}{u^2}\,\mathrm du\,\mathrm dv=2\iint_{D'}\mathrm du\,\mathrm dv$

where $D'$ is the region $D$ transformed into the $u$ - $v$ plane. The remaining integral is the twice the area of $D'$ .

Now, the integral over $D$ is

$\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\left\{\int_0^6\int_{x^2/2}^{x^2}+\int_6^{12}\int_{x^2/2}^{6x}\right\}\frac{\mathrm dx\,\mathrm dy}y$

but through the given transformation, the boundary of $D'$ is the set of equations,

$\begin{array}{l}y=x^2\implies u^2=u^2v^2\implies v^2=1\implies v=\pm1\\y=\frac{x^2}2\implies u^2=\frac{u^2v^2}2\implies v^2=2\implies v=\pm\sqrt2\\y=6x\implies u^2=6uv\implies u=6v\end{array}$

We require that $u>0$ , and the last equation tells us that we would also need $v>0$ . This means $1\le v\le\sqrt2$ and $0$ , so that the integral over $D'$ is

$\displaystyle2\iint_{D'}\mathrm du\,\mathrm dv=2\int_1^{\sqrt2}\int_0^{6v}\mathrm du\,\mathrm dv=\boxed6$

4 0

3 years ago

Given each set of points, determine if AB and CD

tester [92]

Answer:

Paralell

Step-by-step explanation:

The line from A to B has a slope of 1

the Line from C to D had a slope of 1

since the slopes are equal the lines are paralell

7 0

2 years ago

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Pic is question vuygvcutyfvgt

Furkat [3]

Answer:

Step-by-step explanation:

270/9 = 30

Hope This Helps & Good Luck :)

5 0

3 years ago

Use distributive property to calculate the following.

sattari [20]

Answer:

Step-by-step explanation:

1. 2x + y

2. 48 + 60 = 108

3. 840 - 210 = 630

4 0

2 years ago

If it takes 5 men 20hours to brick a house, how long will it take 2 men to do the job if they work at the same rate?

Elden [556K]

To find the contribution of each man (this is a sexist problem as women could work as well, but that’s besides the point) take 5/2 and then multiply that value by 20 and you’ll find it takes 50 hours for two men to do it.

Answer: 50 hours

4 0

4 years ago

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