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Evgesh-ka [11]
3 years ago
6

The depreciating value of a semi-truck can be modeled by y = Ao(0.87)x, where y is the remaining value of the semi, x is the tim

e in years, and it depreciates at 13% per year. What is the value of the truck initially, Ao, and how would the graph change if the initial value was only $67,000?

Mathematics
2 answers:
vampirchik [111]3 years ago
8 0
The value of A_{0} is 87000 since it is the value when t = 0

The graph would cross the y-axis at 67000 for t = 0 which is the initial value 
Bond [772]3 years ago
7 0

Answer: 1)  The value of truck initially would be $87000.

2)  at t = 0 , y-axis would be cut at $67000.

Step-by-step explanation:

Since we have given that

y=A_0(0.87)^x

Here, A₀ is the initial value.

Rate of depreciation = 13%

Number of years = x

So, The value of truck initially would be $87000.

As shown in the given figure.

If the the initial value of truck = $67000

Rate will be same but the y-intercept will change.

As change in initial value does not affect the rate but the y - intercept.

Then at t = 0 , y-axis would be cut at $67000.

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\rightarrow z^4=-625\\\\\rightarrow z=(-625+0i)^{\frac{1}{4}}\\\\\rightarrow x+iy=(-625+0i)^{\frac{1}{4}}\\\\ x=r \cos A\\\\y=r \sin A\\\\r \cos A=-625\\\\ r \sin A=0\\\\x^2+y^2=625^{2}\\\\r^2=625^{2}\\\\|r|=625\\\\ \tan A=\frac{0}{-625}\\\\ \tan A=0\\\\ A=\pi\\\\\rightarrow z= [625(\cos (2k \pi+pi) +i \sin (2k\pi+ \pi)]^{\frac{1}{4}}\\\\k=0,1,2,3,4,....\\\\\rightarrow z=(625)^{\frac{1}{4}}[\cos \frac{(2k \pi+pi)}{4} +i \sin \frac{(2k\pi+ \pi)}{4}]

\rightarrow z_{0}=(625)^{\frac{1}{4}}[\cos \frac{pi}{4} +i \sin \frac{\pi)}{4}]\\\\\rightarrow z_{1}=(625)^{\frac{1}{4}}[\cos \frac{3\pi}{4} +i \sin \frac{3\pi}{4}]\\\\ \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]\\\\ \rightarrow z_{3}=(625)^{\frac{1}{4}}[\cos \frac{7\pi}{4} +i \sin \frac{7\pi}{4}]

Argument of Complex number

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If, x>0, y>0, Angle lies in first Quadrant.

If, x<0, y>0, Angle lies in Second Quadrant.

If, x<0, y<0, Angle lies in third Quadrant.

If, x>0, y<0, Angle lies in fourth Quadrant.

We have to find those roots among four roots whose argument is between 270° and 360°.So, that root is

   \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]

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