Answer:
The half life of the car is 3.98 years.
Step-by-step explanation:
The value of the car after t years is given by the following equation:
![V(t) = V(0)(1-r)^{t}](https://tex.z-dn.net/?f=V%28t%29%20%3D%20V%280%29%281-r%29%5E%7Bt%7D)
In which V(0) is the initial value and r is the constant decay rate, as a decimal.
The value of a certain car decreases by 16% each year.
This means that ![r = 0.16](https://tex.z-dn.net/?f=r%20%3D%200.16)
So
![V(t) = V(0)(1-r)^{t}](https://tex.z-dn.net/?f=V%28t%29%20%3D%20V%280%29%281-r%29%5E%7Bt%7D)
![V(t) = V(0)(1-0.16)^{t}](https://tex.z-dn.net/?f=V%28t%29%20%3D%20V%280%29%281-0.16%29%5E%7Bt%7D)
![V(t) = V(0)(0.84)^{t}](https://tex.z-dn.net/?f=V%28t%29%20%3D%20V%280%29%280.84%29%5E%7Bt%7D)
What is the 1⁄2-life of the car?
This is t for which V(t) = 0.5V(0). So
![V(t) = V(0)(0.84)^{t}](https://tex.z-dn.net/?f=V%28t%29%20%3D%20V%280%29%280.84%29%5E%7Bt%7D)
![0.5V(0) = V(0)(0.84)^{t}](https://tex.z-dn.net/?f=0.5V%280%29%20%3D%20V%280%29%280.84%29%5E%7Bt%7D)
![(0.84)^{t} = 0.5](https://tex.z-dn.net/?f=%280.84%29%5E%7Bt%7D%20%3D%200.5)
![\log{(0.84)^{t}} = \log{0.5}](https://tex.z-dn.net/?f=%5Clog%7B%280.84%29%5E%7Bt%7D%7D%20%3D%20%5Clog%7B0.5%7D)
![t\log{0.84} = \log{0.5}](https://tex.z-dn.net/?f=t%5Clog%7B0.84%7D%20%3D%20%5Clog%7B0.5%7D)
![t = \frac{\log{0.5}}{\log{0.84}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Clog%7B0.5%7D%7D%7B%5Clog%7B0.84%7D%7D)
![t = 3.98](https://tex.z-dn.net/?f=t%20%3D%203.98)
The half life of the car is 3.98 years.
Answer: a) add n+1 to the previous term
b) add the previous two terms
d) subtract n+1 from the previous term
e) multiply the previous term by 3
f) subtract 2 from previous term then add 5 to the next term
<u>Step-by-step explanation:</u>
a) 1, 3, 6, 10
∨ ∨ ∨
+2 +3 +4 The next term is 10 +5 = 15
b) 1, 2, 3, 5
∨ ∨ ∨
=3 =5 =8 The next term is 5 + 8 = 13
d) 8, 7, 5, 2
∨ ∨ ∨
-1 -2 -3 zThe next term is 2 - 4 = -2
e) 1, 3, 9, 27
∨ ∨ ∨
×3 ×3 ×3 The next term is 27 × 3 = 81
f) 49, 47, 52, 50, 55
∨ ∨ ∨ ∨
-2 +5 -2 +5 The next term is 55 - 2 = 53
The following term is 53 + 5 = 58
12. I need the graphs to answer it
11. y = 1/2x - 1
10. The first graph is the best
Answer:
This is english not math but.....
If it is warm outside, then it is summer.
Step-by-step explanation:
Basically just switch the terms and make it grammatically correct.
Answer: The correct answer is <em>-x+3y=6</em>
Step-by-step explanation:
<u>Solve for x:</u>
y=1/3x+2
1) Flip the equation:
1/3x+2=y
2) Add -2 to both sides:
1/3x+2+−2=y+−2
1/3x=y−2
3) Divide both sides by 1/3:
(1/3x)/(1/3)=(y−2)/(1/3)
x=3y−6
In standard form (Ax=By=C): -x+3y=6