The formula for depreciation is:
![y=x(1-r)^t](https://tex.z-dn.net/?f=%20y%3Dx%281-r%29%5Et%20)
Where x = Initial value,
y= Amount after depreciation.
r= Rate of depreciation,
t = time (in years)
According to given problem,
x = 1040, y= 944 and t = 12 months =1 year.
So, first step is to plug in these values in the above formula, So,
![944 = 1040(1-r)^1](https://tex.z-dn.net/?f=%20944%20%3D%201040%281-r%29%5E1%20)
944 = 1040 (1 -r)
Divide each sides by 1040.
0.907692308 =1 - r
0.907692308 - 1 = -r Subtract 1 from each sides.
-0.092307692 = -r
So, r = 0.09 or 9%.
Now plug in 0.09 in the above equation to get the depreciation equation. So,
![y = x (1- 0.09)^t](https://tex.z-dn.net/?f=%20y%20%3D%20x%20%281-%200.09%29%5Et%20)
So, ![y = 0.91x^t](https://tex.z-dn.net/?f=%20y%20%3D%200.91x%5Et%20)
b) To find the value of the bike after 5 months,
plug in t = 5 months= 5/12 = 0.41667 years in the above equation of depreciation.
So, ![y= 1040 *(0.91)^{0.41667}](https://tex.z-dn.net/?f=%20y%3D%201040%20%2A%280.91%29%5E%7B0.41667%7D%20%20)
y = 1040 * 0.961465659
y = 999.9242852
y = 1000 (Rounded to nearest integer).
Hence, the value of the bike after 5 months is $1000.
<h3>After 6 weeks from now you will have $190 in your bank account</h3>
<em><u>Solution:</u></em>
Given that,
You have $55 in your bank account
Each week you deposit $8 from your allowance and $15 from your paycheck
<em><u>The equation that gives the amount b in your account after w weeks is:</u></em>
b = 55 + (15 + 8)w
<em><u>How many weeks from now will you have $190 in your bank account ?</u></em>
b = 190
w = ?
Therefore,
190 = 55 + (15 + 8) w
190 = 55 + 23w
23w = 190 - 55
23w = 135
Divide both sides by 23
![w = 5.869 \approx 6](https://tex.z-dn.net/?f=w%20%3D%205.869%20%5Capprox%206)
Thus after 6 weeks from now you will have $190 in your bank account
Answer:true
Step-by-step explanation:
2000 = 20x100
Answer:
21.4, Because x is starts at 11 ending far away down, which means x has to be longer than 11
Step-by-step explanation:
:b
Answer:
![a=13.59,-0.59](https://tex.z-dn.net/?f=a%3D13.59%2C-0.59)
Step-by-step explanation:
Assuming the question is:
![(a-12)a=a+8](https://tex.z-dn.net/?f=%28a-12%29a%3Da%2B8)
We multiply and rearrange the trinomial:
![(a-12)a=a+8\\a^2-12a=a+8\\a^2-13a-8=0](https://tex.z-dn.net/?f=%28a-12%29a%3Da%2B8%5C%5Ca%5E2-12a%3Da%2B8%5C%5Ca%5E2-13a-8%3D0)
This is a quadratic equation with:
a = 1
b = -13
c = -8
We use quadratic formula to find 2 values of a:
![a^2-13a-8=0\\a=\frac{-b+-\sqrt{b^2 - 4ac} }{2a}\\a=\frac{13+-\sqrt{169 - 4(-8)} }{2}\\a=\frac{13+-\sqrt{201} }{2}\\a=13.59,-0.59](https://tex.z-dn.net/?f=a%5E2-13a-8%3D0%5C%5Ca%3D%5Cfrac%7B-b%2B-%5Csqrt%7Bb%5E2%20-%204ac%7D%20%7D%7B2a%7D%5C%5Ca%3D%5Cfrac%7B13%2B-%5Csqrt%7B169%20-%204%28-8%29%7D%20%7D%7B2%7D%5C%5Ca%3D%5Cfrac%7B13%2B-%5Csqrt%7B201%7D%20%7D%7B2%7D%5C%5Ca%3D13.59%2C-0.59)
These are the 2 values of a:
![a=13.59,-0.59](https://tex.z-dn.net/?f=a%3D13.59%2C-0.59)