Find the exponential model of best fit for the points (-3, 5), (1, 12), (5, 72), (7, 137). Explain how you got your answer. Round values to the nearest hundredth.

Answer 1

To find the exponential model of best fit for the given points, we need to find an equation of the form y = ab^x where a and b are constants to be determined.

Let's begin by plugging in the points (-3, 5), (1, 12), (5, 72), and (7, 137) into the equation y = ab^x:

For the point (-3, 5):
5 = ab^(-3) ----(1)

For the point (1, 12):
12 = ab^1 ----(2)

For the point (5, 72):
72 = ab^5 ----(3)

For the point (7, 137):
137 = ab^7 ----(4)

We can rewrite equations (1), (2), (3), and (4) as:

1. 5 = a/b^3
2. 12 = ab
3. 72 = ab^5
4. 137 = ab^7

To eliminate the variable a, we will take equation (4) divided by equation (2):

(137)/(12)= (ab^7)/(ab)
11.42=b^6
b= (11.42)^(1/6)
b ≈ 1.619

Now substitute the value of b into equation (2):

12 = a * (1.619)
a ≈ 7.40

Therefore, the exponential model of best fit is given by y = 7.40 * (1.619)^x.