Answer:
A(t)= 18000(0.988)^t
Step-by-step explanation:
Given data
Ryan bought a brand new car for $18,000
Its value depreciated at a rate of 1.2%
Let us use the compound expression
A= P(1-r)^t
substitute
A= 18000(1-0.012)^t
A(t)= 18000(0.988)^t
Hence the expression is A(t)= 18000(0.988)^t
Answer:
24
Step-by-step explanation:
6+2×3+4+(27-19)
first the bracket, (27 -19) = 8
and then the multiplication, 2×3 = 6
then the addition, 6+6+4+8 = 24
Answer:
<h2>-223,948</h2>
Step-by-step explanation:
The formula of a sum of terms of a gometric sequence:
![S_n=a_1\cdot\dfrac{1-r^n}{1-r}](https://tex.z-dn.net/?f=S_n%3Da_1%5Ccdot%5Cdfrac%7B1-r%5En%7D%7B1-r%7D)
a₁ - first term
r - common ratio
We have
![a_n=-4(6)^{n-1}](https://tex.z-dn.net/?f=a_n%3D-4%286%29%5E%7Bn-1%7D)
Calculate a₁. Put n = 1:
![a_1=-4(6)^{1-1}=-4(6)^0=-4(1)=-4](https://tex.z-dn.net/?f=a_1%3D-4%286%29%5E%7B1-1%7D%3D-4%286%29%5E0%3D-4%281%29%3D-4)
Calculate the common ratio:
![r=\dfrac{a_{n+1}}{a_n}\\\\a_{n+1}=-4(6)^{n+1-1}=-4(6)^n\\\\r=\dfrac{-4(6)^n}{-4(6)^{n-1}}=6^n:6^{n-1}\\\\\text{use}\ a^n:a^m=a^{n-m}\\\\r=6^{n-(n-1)}=6^{n-n+1}=6^1=6](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7Ba_%7Bn%2B1%7D%7D%7Ba_n%7D%5C%5C%5C%5Ca_%7Bn%2B1%7D%3D-4%286%29%5E%7Bn%2B1-1%7D%3D-4%286%29%5En%5C%5C%5C%5Cr%3D%5Cdfrac%7B-4%286%29%5En%7D%7B-4%286%29%5E%7Bn-1%7D%7D%3D6%5En%3A6%5E%7Bn-1%7D%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%20a%5En%3Aa%5Em%3Da%5E%7Bn-m%7D%5C%5C%5C%5Cr%3D6%5E%7Bn-%28n-1%29%7D%3D6%5E%7Bn-n%2B1%7D%3D6%5E1%3D6)
![\text{Substitute}\ a_1=-4,\ n=7,\ r=6:\\\\S_7=-4\cdot\dfrac{1-6^7}{1-6}=-4\cdot\dfrac{1-279936}{-5}=-4\cdot\dfrac{-279935}{-5}=(-4)(55987)\\\\S_7=-223948](https://tex.z-dn.net/?f=%5Ctext%7BSubstitute%7D%5C%20a_1%3D-4%2C%5C%20n%3D7%2C%5C%20r%3D6%3A%5C%5C%5C%5CS_7%3D-4%5Ccdot%5Cdfrac%7B1-6%5E7%7D%7B1-6%7D%3D-4%5Ccdot%5Cdfrac%7B1-279936%7D%7B-5%7D%3D-4%5Ccdot%5Cdfrac%7B-279935%7D%7B-5%7D%3D%28-4%29%2855987%29%5C%5C%5C%5CS_7%3D-223948)
Step-by-step explanation:
HOPE IT HELPS!!!!!!!!!