Answer:
The growth rate is 0.6
The growth factor is 1.6
Step-by-step explanation:
Generally, the exponential equation can be written as;
y = a(1 + r)^x
Where a is the initial value of 100
r is the growth rate
So let us form equations;
160 = 100(1 + r)^1 •••••(i)
Also;
256 = 100(1 + r)^2 •••••••(ii)
Divide equation ii by i
256/160 = 1 + r
1.6 = 1 + r
r = 1.6-1
r = 0.6
The answers are 3.19 or -2.19.
In order to complete the square, you must first get the constant to the other side of the equation. WE do that by adding 7 to both sides.
x^2 - x - 7 = 0
x^2 - x = 7
Now we must take half of the x coefficient (-1), which would be -.5. Then we square it and add it to both sides. This is the second step to any completing the square problem.
x^2 - x = 7
x^2 - x + .25 = 7.25
Now that we have done that, the left side will be a perfect square so that, we can factor it.
x^2 - x + .25 = 7.25
(x - .5)^2 = 7.25
After having done that, we can take the square root of both sides
(x - .5)^2 = 7.25
x - .5 = +/-
Now we can take the value of that square root and solve.
x - .5 = +/-
x - .5 = +/-2.69
x = .5 +/- 2.69
And with the + and - both there, we need to do both to get the two answers.
.5 + 2.69 = 3.19
.5 - 2.69 = -2.19
We see it is the y terms squared so it opens left or right
in form
(y-k)^2=4(p)(x-h)
vertex is (h,k)
and p is distance from focus to vertex, also distance from vertex to directix
if p>0, then it opens to the right and dirextix is to the left of vertex
if p<0, then it opens to the left and directix is tothe right of vertex
so
(y-1)^2=4(4)(x-(-3))
vertex is (-3,1)
4>0 so dirextix is to left of vertex
left is in x direction
-3-4=-7
directix is x=-7
Answer: 1.5 inches/hour
Step-by-step explanation:
4.5/3=