Answer:
The 38th term of 459,450,441,.. will be:
![a_{13}=351](https://tex.z-dn.net/?f=a_%7B13%7D%3D351)
Step-by-step explanation:
Given the sequence
![459,450,441,..](https://tex.z-dn.net/?f=459%2C450%2C441%2C..)
An arithmetic sequence has a constant difference 'd' and is defined by
![a_n=a_1+\left(n-1\right)d](https://tex.z-dn.net/?f=a_n%3Da_1%2B%5Cleft%28n-1%5Cright%29d)
computing the differences of all the adjacent terms
![450-459=-9,\:\quad \:441-450=-9](https://tex.z-dn.net/?f=450-459%3D-9%2C%5C%3A%5Cquad%20%5C%3A441-450%3D-9)
so
![d=-9](https://tex.z-dn.net/?f=d%3D-9)
The first element of the sequence is
![a_1=459](https://tex.z-dn.net/?f=a_1%3D459)
so the nth term will be
![a_n=-9\left(n-1\right)+459](https://tex.z-dn.net/?f=a_n%3D-9%5Cleft%28n-1%5Cright%29%2B459)
![a_n=-9n+468](https://tex.z-dn.net/?f=a_n%3D-9n%2B468)
Putting n=38 to find the 38th term
![a_n=-9n+468](https://tex.z-dn.net/?f=a_n%3D-9n%2B468)
![a_{13}=-9\left(13\right)+468](https://tex.z-dn.net/?f=a_%7B13%7D%3D-9%5Cleft%2813%5Cright%29%2B468)
![a_{13}=-117+468](https://tex.z-dn.net/?f=a_%7B13%7D%3D-117%2B468)
![a_{13}=351](https://tex.z-dn.net/?f=a_%7B13%7D%3D351)
Therefore, the 38th term of 459,450,441,.. will be:
![a_{13}=351](https://tex.z-dn.net/?f=a_%7B13%7D%3D351)
Answer:
f(t) = 1.22·(173/122)^(t/5)
Step-by-step explanation:
(a) An exponential growth (or decay) function can be written using the form ...
f(t) = (initial value)·(ratio in period)^(t/period)
Here, we're given an initial value of 1.22, a growth ratio of 1.73/1.22 in a period of 5 years, so we can write the function as ...
f(t) = 1.22·(173/122)^(t/5)
__
(b) In 2038-2012 = 26 years, the value of the function is ...
f(26) = 1.22·(173/122)^(26/5) ≈ 7.50 . . . . million
Answer:
$3.84
Step-by-step explanation
move the decimal back two place - .28, it is a mark up so add a 1 at the beginning - 1.28 - multiply - 3 x 1.28 = 3.84
Answer:
Equation have Unique solution i.e ![x=-20](https://tex.z-dn.net/?f=x%3D-20)
Step-by-step explanation:
Given Equation:
![-6(x+7)=-4x-2](https://tex.z-dn.net/?f=-6%28x%2B7%29%3D-4x-2)
Solving the Equation for 'x'.
![-6(x)-6(7)=-4x-2\\\\-6x-42=-4x-2](https://tex.z-dn.net/?f=-6%28x%29-6%287%29%3D-4x-2%5C%5C%5C%5C-6x-42%3D-4x-2)
Adding '
' both sides:
![-6x+4x-42=-4x+4x-2\\\\-6x+4x-42=-2\\\\-2x-42=-2](https://tex.z-dn.net/?f=-6x%2B4x-42%3D-4x%2B4x-2%5C%5C%5C%5C-6x%2B4x-42%3D-2%5C%5C%5C%5C-2x-42%3D-2)
Adding '42' both sides:
![-2x-42+42=-2+42\\\\-2x=40](https://tex.z-dn.net/?f=-2x-42%2B42%3D-2%2B42%5C%5C%5C%5C-2x%3D40)
![x=\frac{40}{-2} \\\\x=-20](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B40%7D%7B-2%7D%20%5C%5C%5C%5Cx%3D-20)
The equation have Unique solution with the value of ![x=-20](https://tex.z-dn.net/?f=x%3D-20)