Let 
. Then differentiating, we get
We approximate 
at 
with the tangent line,
The 
-intercept for this approximation will be our next approximation for the root,
Repeat this process. Approximate at 
.
Then
Once more. Approximate at 
.
Then
Compare this to the actual root of , which is approximately <u>1.76929</u>2354, matching up to the first 5 digits after the decimal place.
Answer: 7
Step-by-step explanation: it just makes sense
You do Y2-Y1 Divided by X2-X1
Let us model this problem with a polynomial function.
Let x = day number (1,2,3,4, ...)
Let y = number of creatures colled on day x.
Because we have 5 data points, we shall use a 4th order polynomial of the form
y = a₁x⁴ + a₂x³ + a₃x² + a₄x + a₅
Substitute x=1,2, ..., 5 into y(x) to obtain the matrix equation
| 1 1 1 1 1 | | a₁ | | 42 |
| 2⁴ 2³ 2² 2¹ 2⁰ | | a₂ | | 26 |
| 3⁴ 3³ 3² 3¹ 3⁰ | | a₃ | = | 61 |
| 4⁴ 4³ 4² 4¹ 4⁰ | | a₄ | | 65 |
| 5⁴ 5³ 5² 5¹ 5⁰ | | a₅ | | 56 |
When this matrix equation is solved in the calculator, we obtain
a₁ = 4.1667
a₂ = -55.3333
a₃ = 253.3333
a₄ = -451.1667
a₅ = 291.0000
Test the solution.
y(1) = 42
y(2) = 26
y(3) = 61
y(4) = 65
y(5) = 56
The average for 5 days is (42+26+61+65+56)/5 = 50.
If Kathy collected 53 creatures instead of 56 on day 5, the average becomes
(42+26+61+65+53)/5 = 49.4.
Now predict values for days 5,7,8.
y(6) = 152
y(7) = 571
y(8) = 1631
Answer:
Increase?
Step-by-step explanation:
Because think about it let's use 1/2 as an example.
1/2 equals .5 now lets add 2 to both the numerator and denominator
3/4 is the result and it also equals .75 which is larger than .5 so that's why the answer is increase.
and u can keep on going on with the method
4/5=.8
