s 1 2 3 4 5 6 r 16 13 12 23 56 1 Which equation represents the relationship between r and s?

The table shows the relationship between r and s, where s is the

did even help

did not help me.😐

To find the equation representing the relationship between r and s, we need to look for a pattern or trend in the given data points.

We can start by plotting the data points on a graph:

s r
1 16
2 13
3 12
4 23
5 56
6 1

Now, let's observe the pattern in the data points. We can see that as s increases, r does not change uniformly. Therefore, this relationship is not linear.

Next, let's try to check if there is a relationship that can be represented by a quadratic equation. To check this, we can square the values of 's' and see if we get a relationship with 'r'.

s^2 r
1 16
4 13
9 12
16 23
25 56
36 1

By calculating the squares of 's' and comparing with 'r', it is evident that there is no consistent relationship between 's^2' and 'r'. Therefore, this relationship is not quadratic.

Since the relationship is not linear or quadratic, we can try to check if there is an exponential relationship between 's' and 'r'. To do that, we can try to take the log of 'r' and plot it against 's'.

s log(r)
1 2.772
2 2.564
3 2.484
4 3.135
5 4.025
6 0

By calculating the logarithm of 'r' and plotting it against 's', we can see that there is a linear relationship between the logarithm of 'r' and 's'. So, the relationship between 'r' and 's' can be represented as:

log(r) = mx + c,

where 'm' represents the slope and 'c' represents the constant term.

To find the values of 'm' and 'c', we can calculate them from the given data points:

Using two points from the data, (s=1, log(r)=2.772) and (s=2, log(r)=2.564):

m = (log(r2) - log(r1))/(s2 - s1)

m = (2.564 - 2.772)/(2 - 1)

m = -0.208

c can be calculated by substituting the values of 'm' and one of the points in the equation:

2.772 = -0.208(1) + c

c = 2.98

Therefore, the equation representing the relationship between 'r' and 's' is:

log(r) = -0.208s + 2.98.

To get r, you can take the antilogarithm (exponentiation) of both sides of the equation:

r = e^(-0.208s + 2.98)

So, the equation representing the relationship between 'r' and 's' is approximately:

r = e^(-0.208s + 2.98).

didnt even help

Well, it's not linear or exponential or sinusoidal, so the next thing to try is polynomial. Not easy, the way it rises and falls so unevenly. It will have to be at least degree 5, so good luck with that. I get

r(s) = -s^5 + 15s^4 - 250/3 s^3 + 216s^2 - 785/3 s + 131