Okay so where's the math question(s)?
Answer:
a
Step-by-step explanation:
Get the slope:
( 10-(-2) )/( 3 - (-1) ) = 3
Let's use letters to represent the ?'s.
y + k = m(x + 1)
Examine the equation:
Notice that if x were to equal -1, the equation would be equal to 0.
m(-1 + 1) = m(0) = 0
If x were to be -1, then y would have to be -2 since that is one of the points provided in the problem.
So now we have:
-2 + k = 0
Solve for k:
k = 2
So I know that 2 is the only number that will work for k.
Our new equation is y + 2 = m(x + 1)
Recall point slope form:
y - y1 = m(x - x1)
Our equation is in the same form as point slope form, so we know that m in our equation represents the slope.
We found the slope at the beginning, it was 3. So plug it in:
y + 2 = 3(x + 1)
Let's test our answer by plugging in a point. Let's try (3, 10):
10 + 2 = 3(3 + 1)
12 = 12
So our answer is correct:
y + 2 = 3(x + 1) is the answer.
To test if linear model, we fit the data into a line and solve for the correlation coefficient:
The equation is
y = -1537.5x + 5466.67
and the correlation coefficient is
R² = 0.964
The model can't be exponential growth since the daily supply decreases with time. So, the data is tested if it's exponential decay. The same procedure is done the exponential equation would be linearized in the form:
y = -2816.06 lnx + 4073.57
with correlation coefficient of
R² = 0.998
Since the correlation coefficient for the exponential decay model is closer to 1, it must be the right model.
