Which kind of function best models the data in the table use differences or ratios.
x y
0, 1.3
1, 7.8
2, 46.8
3, 280.8
4, 1684.8
A) linear
B) quadratic****
C) exponential
D) none of the above
7.8 / 1.3 = 6
46.8 / 7.8 = 6
280.8 / 46.8 = 6
1684.8 / 280.8 = 6
Your data for y is a geometric sequence
( a sequence of numbers in which the ratio between consecutive terms is constant).
The n-th term of a geometric sequence with initial value a1 and common ratio r is given by:
an = a1 ∙ r ⁿ⁻¹
In this case a1 = 1.3 , r = 6
an = 1.3 ∙ 6 ⁿ⁻¹
This mean your function is:
y = 1.3 ∙ 6 ˣ⁻¹
1.3 ∙ 6 ˣ⁻¹ is exponential function
Answer C
thx Bosnian
0 1.7
1 6.8
2 27.2
3 108.2
4 435.2
What kind of equation is this?
nope. Check and you will see that each value is multiplied by 6 to get the next in the list.
quadratic relations have a constant 2nd difference.
Which kind of function best models the data in the table? Use differences or ratios.
x y
0 1.3
1 7.8
2 46.8
3 280.8
4 1684.8
The ratio between consecutive terms of y is constant, which indicates an exponential function best models the data.
So, an exponential function equation with the form y = ab^x where a and b are constants is:
y = 1.3 * 6^x
Therefore, the answer is C) exponential.
To determine which kind of function best models the data in the table, we can analyze the differences or ratios between the values of y as x increases.
1) Using Differences:
- Calculate the differences between consecutive y values:
7.8 - 1.3 = 6.5
46.8 - 7.8 = 39
280.8 - 46.8 = 234
1684.8 - 280.8 = 1404
The differences are not consistent, which suggests that the function is not linear.
2) Using Ratios:
- Calculate the ratios between consecutive y values:
7.8 / 1.3 ≈ 6
46.8 / 7.8 ≈ 6
280.8 / 46.8 ≈ 6
1684.8 / 280.8 ≈ 6
The ratios between the values of y are approximately constant, indicating that the function could be quadratic or exponential.
Based on the ratios, it is more likely that a quadratic function best models the data in the table. Therefore, the correct answer would be B) quadratic.