Help!!! Please!!!!!!

Computing growth rates (I): Suppose Xt=(1.04)^t and Yt=(1.02)^tCalculate the growth rate of Zt in each of the following cases:(a

Doss [256]

Answer:

$z(t) = (0.9808)^t$

$z(t) = (1.0196)^t$

$z(t) = (0.9808)^t$

$z(t) = (1.03)^t$

$z(t) = (1.0404)^t$

$z(t) = (1.0001)^t$

Step-by-step explanation:

We are given the following in the question:

$x(t)=(1.04)^t\\y(t)t=(1.02)^t$

We have to find the growth rate z(t) in each of the following cases:

(a) z = xy

$z(t) = x(t)y(t)\\z(t) = (1.04)^t.(1.02)^t\\z(t) = (1.04\times 1.02)^t\\z(t) = (1.0608)^t$

(b) z=x/y

$z(t) =\displaystyle\frac{x(t)}{y(t)}\\\\z(t) = \frac{(1.04)^t}{(1.02)^t} = \bigg(\frac{1.04}{1.02}\bigg)^t\\\\z(t) = (1.0196)^t$

(c) z=y/x

$z(t) =\displaystyle\frac{y(t)}{x(t)}\\\\z(t) = \frac{(1.02)^t}{(1.04)^t} = \bigg(\frac{1.02}{1.04}\bigg)^t\\\\z(t) = (0.9808)^t$

(d) z=x^(1/2) y^(1/2)

$z(t) = (x(t))^{\frac{1}{2}}(y(t))^{\frac{1}{2}}\\z(t) = ((1.04)^t)^\frac{1}{2} ((1.02)^t)^\frac{1}{2}\\z(t) = (1.0608)^{\frac{t}{2}}\\z(t) = (1.03)^t$

(e) z=(x/y)^2

$z(t) =\bigg(\displaystyle\frac{x(t)}{y(t)}\bigg)^2\\\\z(t) =\bigg( \frac{(1.04)^t}{(1.02)^t}\bigg)^2 = \bigg(\frac{1.04}{1.02}\bigg)^{2t}\\\\z(t) = (1.0404)^t$

(f) z=x^(-1/3)y^(2/3)

$z(t) = (x(t))^{\frac{-1}{3}}(y(t))^{\frac{2}{3}}\\z(t) = ((1.04)^t)^{\frac{-1}{3}}((1.02)^t)^{\frac{2}{3}}\\z(t) = ((1.04)^{\frac{-1}{3}})^t((1.02)^{\frac{2}{3}})^t\\z(t) = (1.04^{\frac{-1}{3}}\times 1.02^{\frac{2}{3}})^t\\z(t) = (1.0001)^t$

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Do a + a + a + a and 4a a have the same value for any value of ? Explain how you know.

katrin2010 [14]

Yes

Because:

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steposvetlana [31]

Answer:

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Step-by-step explanation:

The first step is to find the slope

m = (y2-y1)/ (x2-x1)

= (5-0)/(-2--2)

= (5-0) /(-2+2)

= 5/0

The slope is undefined

That means it is a vertical line (up and down) The x value does not change

x=-2

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Step-by-step explanation:

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