Look at this table:
x y
–
2 1.2
–
1 2.4
0 4.8
1 9.6
2 19.2
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
Looking at the data, it seems to be increasing exponentially. So, the function that models the data is an exponential function.
In an exponential function, the general form is y = a(b)^x, where a represents the initial value and b represents the growth rate.
To find the values of a and b, we can look at the given data:
- When x = 0, y = 4.8.
- When x = 1, y = 9.6.
Using these values, we can create two equations:
Equation 1: 4.8 = a(b)^0 = a(1) = a
Equation 2: 9.6 = a(b)^1 = ab
Simplifying Equation 2 by substituting Equation 1, we get:
9.6 = 4.8b
b = 9.6 / 4.8 = 2
Substituting the value of b back into Equation 1, we get:
a = 4.8
Therefore, the exponential function that models the data is y = 4.8(2)^x.