Use the exponential regression equation that best fits (10,4), (12,20), (13,35), and (16,300) to estimate the value of y when x = 14.
A. 48.4
B. 73.5
C. 132.3
D. 223.7
The exponential regression equation can be expressed as:
y = ab^x
To determine the values of a and b, let's use the given data points.
For the point (10, 4):
4 = ab^10
For the point (12, 20):
20 = ab^12
For the point (13, 35):
35 = ab^13
For the point (16, 300):
300 = ab^16
Solving this system of equations, we find that a ≈ 1.301 and b ≈ 1.496.
Now, to estimate the value of y when x = 14:
y = ab^14
y ≈ 1.301 * (1.496)^14
y ≈ 1.301 * 223.7
y ≈ 290.351
The estimated value of y when x = 14 is approximately 290.351.
The closest option to this value is D. 223.7.