Look at this table:
x y
1 7.76
2 15.52
3 31.04
4 62.08
5 124.16
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine whether the relationship between x and y is linear or exponential, we can analyze the data.
When x increases by 1, y is multiplied by 2. This is indicative of an exponential relationship, as the variable x is the exponent.
To find the exponential function that models the data, we can use the formula y = a(b)^x.
Analyzing the data, we can see that when x = 1, y = 7.76. Plugging these values into the exponential function, we get:
7.76 = a(b)^1
Simplifying, we have:
7.76 = ab
Next, let's analyze the data when x = 2. We have y = 15.52. Plugging these values into the exponential function, we get:
15.52 = a(b)^2
Now, we have two equations:
7.76 = ab ...(1)
15.52 = a(b)^2 ...(2)
To solve this system of equations, we can divide equation (2) by equation (1):
(15.52)/(7.76) = (a(b)^2)/(ab)
2 = b
Substituting this value of b into equation (1), we get:
7.76 = a(2)
Simplifying, we find:
3.88 = a
Therefore, the exponential function that models the data is:
y = 3.88(2)^x