Answer:
The function to determine the value of your car (in dollars) in terms of the number of years t since 2012 is:
![f(t) = 10000(0.9407)^t](https://tex.z-dn.net/?f=f%28t%29%20%3D%2010000%280.9407%29%5Et)
Step-by-step explanation:
Value of the car:
Constant rate of change, so the value of the car in t years after 2012 is given by:
![f(t) = f(0)(1-r)^t](https://tex.z-dn.net/?f=f%28t%29%20%3D%20f%280%29%281-r%29%5Et)
In which f(0) is the initial value and r is the decay rate, as a decimal.
In 2012 your car was worth $10,000.
This means that
, thus:
![f(t) = 10000(1-r)^t](https://tex.z-dn.net/?f=f%28t%29%20%3D%2010000%281-r%29%5Et)
2014 your car was worth $8,850.
2014 - 2012 = 2, so:
![f(2) = 8850](https://tex.z-dn.net/?f=f%282%29%20%3D%208850)
We use this to find 1 - r.
![f(t) = 10000(1-r)^t](https://tex.z-dn.net/?f=f%28t%29%20%3D%2010000%281-r%29%5Et)
![8850 = 10000(1-r)^2](https://tex.z-dn.net/?f=8850%20%3D%2010000%281-r%29%5E2)
![(1-r)^2 = \frac{8850}{10000}](https://tex.z-dn.net/?f=%281-r%29%5E2%20%3D%20%5Cfrac%7B8850%7D%7B10000%7D)
![(1-r)^2 = 0.885](https://tex.z-dn.net/?f=%281-r%29%5E2%20%3D%200.885)
![\sqrt{(1-r)^2} = \sqrt{0.885}](https://tex.z-dn.net/?f=%5Csqrt%7B%281-r%29%5E2%7D%20%3D%20%5Csqrt%7B0.885%7D)
![1 - r = 0.9407](https://tex.z-dn.net/?f=1%20-%20r%20%3D%200.9407)
Thus
![f(t) = 10000(1-r)^t](https://tex.z-dn.net/?f=f%28t%29%20%3D%2010000%281-r%29%5Et)
![f(t) = 10000(0.9407)^t](https://tex.z-dn.net/?f=f%28t%29%20%3D%2010000%280.9407%29%5Et)
It will be 75$ i guess the question is a bit wrong please recheck
Answer:
15% off $30
Step-by-step explanation:
Answer: The wholesale cost of the bike = $100
Step-by-step explanation:
Let x = wholesale cost of the bike
As per given,
Selling price = cost price + (Mark up percent) x ( cost price) (i)
Selling price of bike = $160
Mark up percent = 60% =0.60
Substitute values in (i) , we get
![160= x+0.6x\\\\\Rightarrow\ 160=1.6x\\\\\Rightarrow\ x=\dfrac{160}{1.6}\\\\\Rightarrow\ x= 100](https://tex.z-dn.net/?f=160%3D%20x%2B0.6x%5C%5C%5C%5C%5CRightarrow%5C%20160%3D1.6x%5C%5C%5C%5C%5CRightarrow%5C%20x%3D%5Cdfrac%7B160%7D%7B1.6%7D%5C%5C%5C%5C%5CRightarrow%5C%20x%3D%20100)
Hence, the wholesale cost of the bike = $100