3 - A
4 - C
Ques 3: From the table, we see that,
The slope of the points are given by,
Thus, the equation of the function is, .
So, the best function for this model is a linear function.
Hence, option A is correct.
Ques 4: From the table, we have,
The change in the y-values is,
Thus, the equation of the function is,
Hence, the best function for the model is an exponential function.
So, option C is correct.
If the function is linear, the differences will be equal.
d₁ = y₁ − y₀ = 4.2 − 0.6 = 3.6
d₂ = y₂ − y₁ = 29.4 − 4.2 = 25.2
d₃ = y₃ − y₂ = 205.8 − 29.4 = 176.4
d₄ = y₄ − y₃ = 1440.6 − 205.8 = 1234.8
The differences are not equal, so this is not linear.
If the function is quadratic, the differences of the differences will be equal.
d₂ − d₁ = 25.2 − 3.6 = 21.6
d₃ − d₂ = 176.4 − 25.2 = 151.2
d₄ − d₃ = 1234.8 − 176.4 = 1058.4
The differences of the differences are not equal, so this is not quadratic.
If the function is exponential, the ratios will be equal.
r₁ = y₁ / y₀ = 4.2 / 0.6 = 7
r₂ = y₂ / y₁ = 29.4 / 4.2 = 7
r₃ = y₃ / y₂ = 205.8 / 29.4 = 7
r₄ = y₄ / y₃ = 1440.6 / 205.8 = 7
The ratios are equal, so the function is exponential.
hi im here to help a kid that ask me to help him
Option C exponential.
To find the function best models the data in the table we will find the common ratio first. If the common ratios of the function are same then it's an exponential function.
For x = 0 and x = 1
For x = 1 and x = 2
For x = 2 and x = 3
Now we are sure that it's an exponential function.
For linear function common difference should be same in each term.
f(1) - f(0) = 6.8 - 1.7 = 5.1
f(2) - f(1) = 27.2 - 6.8 = 20.4
Therefore it's neither a linear function nor quadratic function.
Option C. is the correct option.
You can use some graph tools to draw three regressions for given data. On the attached diagram you can see:linear function - black line;quadratic function - red curve;exponential function - blue curve.
you can conclude that for the given data the best fit is exponential function with rule
correct choice is C.
If you look at the values on the left, the x-values, you can see that they are neatly lined up for us and they are increasing by 1.
Now, look at the y-values, they are increasing by adding 1/2.
When you have a constant increase of a value by addition or subtraction, it will create a linear pattern. You can also graph the equation to see the linear pattern.
We are given . This can be rewritten as .
Therefore, a=1, b=-18, c=0.
Using the quadratic formula
The values of x are
Since the values of y change drastically for every equal interval of x, the function cannot be linear. Therefore, the kind of function that best suits the given pairs is a quadratic function.
The first equation is .
The second equation is .
Factoring, we have
Equating both factors to zero.
When the value of x is 6, the value of y is
When the value of x is -3, the value of y is
Therefore, the solutions are (6,38) or (-3,11)
people grow faster than other people.
should you really be posting this isn't math boi.