Using the exponential function, it is found that the SUV is worth $3,253.36 less than the car after 5 years.
The <em>exponential function</em> for the value of the SUV, after x years, is given by:
![f(x) = 17000(0.87)^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%2017000%280.87%29%5Ex)
Hence, after 5 years, the value is:
![f(5) = 17000(0.87)^5 = 8473.16](https://tex.z-dn.net/?f=f%285%29%20%3D%2017000%280.87%29%5E5%20%3D%208473.16)
From the table, after 5 years, the car is worth $11,726.52.
11726.52 - 8473.16 = 3253.36.
The SUV is worth $3,253.36 less than the car after 5 years.
To learn more about exponential functions, you can take a look at brainly.com/question/25983065
According to the use of binomial expansion, the approximate value of √3 is found by applying the infinite sum √3 = 1 + (1 /2) · 2 - (1 / 8) · 2² + (1 / 16) · 2³ - (5 / 128) · 2⁴ + (7 / 256) · 2⁵ - (21 / 1024) · 2⁶ + (33 / 2048) · 2⁷ - (429 / 32768) · 2⁸ +...
An acceptable result cannot be found manually for it requires a <em>high</em> number of elements, with the help of a solver we find that the <em>approximate</em> value of √3 is 1.732.
<h3>How to approximate the value of a irrational number by binomial theorem</h3>
Binomial theorem offers a formula to find the <em>analytical</em> form of the power of a binomial of the form (a + b)ⁿ:
(1)
Where:
- a, b - Constants of the binomial.
- n - Grade of the power binomial.
- k - Index of the k-th element of the power binomial.
If we know that a = 1, b = 2 and n = 1 / 2, then an approximate expression for the square root is:
√3 = 1 + (1 /2) · 2 - (1 / 8) · 2² + (1 / 16) · 2³ - (5 / 128) · 2⁴ + (7 / 256) · 2⁵ - (21 / 1024) · 2⁶ + (33 / 2048) · 2⁷ - (429 / 32768) · 2⁸ +...
To learn more on binomial expansions: brainly.com/question/12249986
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Answer (<u>assuming it can be written in slope-intercept form)</u>:
![y = \frac{7}{9} x+\frac{17}{9}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B7%7D%7B9%7D%20x%2B%5Cfrac%7B17%7D%7B9%7D)
Step-by-step explanation:
1) First, find the slope of the line. Use the slope formula,
. Substitute the x and y values of the given points into the formula and solve:
So, the slope is
.
2) Now, use the point-slope formula
to write the equation of the line. Substitute
,
, and
for real values.
Since
represents the slope, substitute
for it. Since
and
represent the x and y values of one point the line intersects, choose from any one of the given points (it doesn't matter which one, either way the result equals the same thing) and substitute its x and y values into the formula as well. (I chose (4,5), as seen below.) From there, isolate y to place the equation in slope-intercept form (
format) and find the following answer:
Subtract second y from first y and divide that by second x from first x
1-2=-1
3- -5=3+5= 8
so, -1/8
this is your m= -1/8
now pick one of the points and add it to your point intercept form (I'm picking (3,1))
y-1= -1/8 (x-3)
y-1= -1/8x - (-1/8×3)
y-1= -1/8x +3/8
y= -1/8x +3/8+1
y= -1/8x +11/8
Answer:
-49 275/1000
Step-by-step explanation: