A = P(1 + r)^n; where A is the amount after time, n; P is the principal (the invested amount); r is the interest rate and n is the number of periods (i.e. no of years since the amount is compounded annually).
8000 = 4000(1 + 5/100)^n
8000/4000 = (1 + 0.05)^n
(1.05)^n = 2
n log 1.05 = log 2
n = log 2 / log 1.05 = 14.2067
Therefore, the amount will double in approximately 14 years.
Answer:
Part 1) The vertex is the point (-83,-9)
Part 2) The focus is the point (-82.75,-9)
Part 3) The directrix is ![x=-83.25](https://tex.z-dn.net/?f=x%3D-83.25)
Step-by-step explanation:
step 1
Find the vertex
we know that
The equation of a horizontal parabola in the standard form is equal to
![(y - k)^{2}=4p(x - h)](https://tex.z-dn.net/?f=%28y%20-%20k%29%5E%7B2%7D%3D4p%28x%20-%20h%29)
where
p≠ 0.
(h,k) is the vertex
(h + p, k) is the focus
x=h-p is the directrix
In this problem we have
![x=y^{2} +18y-2](https://tex.z-dn.net/?f=x%3Dy%5E%7B2%7D%20%2B18y-2)
Convert to standard form
![x+2=y^{2} +18y](https://tex.z-dn.net/?f=x%2B2%3Dy%5E%7B2%7D%20%2B18y)
![x+2+81=y^{2} +18y+81](https://tex.z-dn.net/?f=x%2B2%2B81%3Dy%5E%7B2%7D%20%2B18y%2B81)
![x+83=(y+9)^{2}](https://tex.z-dn.net/?f=x%2B83%3D%28y%2B9%29%5E%7B2%7D)
so
This is a horizontal parabola open to the right
(h,k) is the point (-83,-9)
so
The vertex is the point (-83,-9)
step 2
we have
![x+83=(y+9)^{2}](https://tex.z-dn.net/?f=x%2B83%3D%28y%2B9%29%5E%7B2%7D)
<em>Find the value of p</em>
![4p=1](https://tex.z-dn.net/?f=4p%3D1)
![p=1/4](https://tex.z-dn.net/?f=p%3D1%2F4)
<em>Find the focus</em>
(h + p, k) is the focus
substitute
(-83+1/4,-9)
The focus is the point (-82.75,-9)
step 3
Find the directrix
The directrix of a horizontal parabola is
![x=h-p](https://tex.z-dn.net/?f=x%3Dh-p)
substitute
![x=-83-1/4](https://tex.z-dn.net/?f=x%3D-83-1%2F4)
![x=-83.25](https://tex.z-dn.net/?f=x%3D-83.25)
Answer:
![f(x)=-(x+2)(x-.5)(x-3)](https://tex.z-dn.net/?f=f%28x%29%3D-%28x%2B2%29%28x-.5%29%28x-3%29)
This polynomial could have infinite possibilities as any negative leading coefficient will satisfy this criteria.
To get this answer you got to multiply each answer by .20% and then subtract the answer from what you divided .20% by and you should get the answer which is 88.002
Answer:
Y = 2X + 19
Step-by-step explanation:
the relationship is linear
gradient equals 2