Look at this table:x y–1 0.860 2.581 7.742 23.223 69.66Write a linear (y=mx+b), quadratic (y=ax2), or exponential (y=a(b)x) function that models the data.y=
Question
Look at this table:
| x | y |
|---|---|
| 1 | 0.860 |
| 2 | 2.581 |
| 3 | 7.742 |
| 4 | 23.223 |
| 5 | 69.66 |
Write a linear (y=mx+b), quadratic (y=ax^2), or exponential (y=a(b)^x) function that models the data.
y=
Solution
The given data seems to follow an exponential model, as the y-values are increasing at an increasing rate.
To write an exponential function that models the data, we can use the form y = a(b)^x.
Looking at the data, when x = 0, y = 2.58. This gives us the initial value 'a'.
So, a = 2.58.
To find the base 'b', we can take the ratio of two consecutive y-values. For example, when x = 1, y = 7.74, and when x = 2, y = 23.22.
So, b = 23.22 / 7.74 ≈ 3.
Therefore, the exponential function that models the data is y = 2.58(3)^x.
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