Answer:
or
Step-by-step explanation:
We are going to see if the exponential curve is of the form:
, (
).
If you are given the 
intercept, then 
is easy to find.
It is just the coordinate of the intercept is your value for .
(Why? The intercept happens when 
. Replacing 
with 0 gives 
. This says when 
.)
So 
.
So our function so far looks like this:
Now to find 
we need another point. We have two more points. So we will find using one of them and verify for our resulting equation works for the other.
Let's do this.
We are given 
is a point on our curve.
So when 
, 
.
Divide both sides by 8:
Reduce the fraction:
So the equation if it works out for the other point given is:
Let's try it. So the last point given that we need to satisfy is 
.
This says when 
, 
.
Let's replace with 2 and see what we get for 
:
So we are good. We have found an equation satisfying all 3 points given.
The equation is .
Answer:
...
Step-by-step explanation:
Answer: 20%
1/(1+4) = the answer
its just the amount of lemon juice over total volume
You need to understand that you're solving for the average, which you already know: 90. Since you know the values of the first three exams, and you know what your final value needs to be, just set up the problem like you would any time you're averaging something.
Solving for the average is simple:
Add up all of the exam scores and divide that number by the number of exams you took.
(87 + 88 + 92) / 3 = your average if you didn't count that fourth exam.
Since you know you have that fourth exam, just substitute it into the total value as an unknown, X:
(87 + 88 + 92 + X) / 4 = 90
Now you need to solve for X, the unknown:
87
+
88
+
92
+
X
4
(4) = 90 (4)
Multiplying for four on each side cancels out the fraction.
So now you have:
87 + 88 + 92 + X = 360
This can be simplified as:
267 + X = 360
Negating the 267 on each side will isolate the X value, and give you your final answer:
X = 93
Now that you have an answer, ask yourself, "does it make sense?"
I say that it does, because there were two tests that were below average, and one that was just slightly above average. So, it makes sense that you'd want to have a higher-ish test score on the fourth exam.
