To determine if the data can be modeled by a linear or exponential function, we need to examine the relationship between the x and y values.
If the y values increase or decrease at a constant rate as the x values increase, then the data can be modeled by a linear function.
If the ratio of the y values to the x values remains constant as the x values increase, then the data can be modeled by an exponential function.
Let's calculate the ratios:
For the given table,
Ratio between y and x for each row:
17/4 = 4.25
23/5 = 4.6
29/6 = 4.83
35/7 = 5
41/8 = 5.125
The ratios are not constant, suggesting that the data cannot be modeled by an exponential function.
Thus, we need to try modeling the data with a linear function. Let's calculate the slope (m) and y-intercept (b) using the formula for a linear function:
m = (y2-y1)/(x2-x1)
Using the points (4, 17) and (8, 41):
m = (41-17)/(8-4)
= 24/4
= 6
Now, to find b, we can use the equation y = mx + b and substitute one of the given points. Let's use (4, 17):
17 = 6(4) + b
17 = 24 + b
17 - 24 = b
-7 = b
So the linear function that models the data is:
y = 6x - 7
Look at this table:
x y
4 17
5 23
6 29
7 35
8 41
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
1 answer