The exponential regression equation can be written in the form y = ab^x, where a and b are constants to be determined.
To find the values of a and b, we can use the given data points. We will set up a system of equations based on these points.
Using the first data point (10, 4), we get:
4 = ab^10
Using the second data point (12, 20), we get:
20 = ab^12
Using the third data point (13, 35), we get:
35 = ab^13
Using the fourth data point (16, 300), we get:
300 = ab^16
To solve this system of equations, we can divide each equation by the equation before it:
(20)/(4) = (ab^12)/(ab^10)
5 = b^2
(35)/(20) = (ab^13)/(ab^12)
1.75 = b
(300)/(35) = (ab^16)/(ab^13)
8.57 = b^3
Now we can solve for b by taking the square root of 5 (from b^2 = 5), which gives us b ≈ 2.236. Taking the cube root of 8.57 (from b^3 = 8.57), we get approximately b ≈ 2.116.
Now that we have the value of b, we can substitute it into any of the original equations to solve for a. Let's use the first equation (4 = ab^10):
4 = a(2.236)^10
4 = 102.595a
a ≈ 0.0389
So the exponential regression equation that best fits the data is y ≈ 0.0389(2.236)^x.
To estimate the value of y when x = 14, we substitute this value into the equation:
y ≈ 0.0389(2.236)^14
y ≈ 0.0389(227.57)
y ≈ 8.8497
Therefore, the estimated value of y when x = 14 is approximately 8.8497.
None of the given answer choices (48.4, 73.5, 132.3, 223.7) match this estimation, so none of the provided options (a, b, c, d) are correct.
Use the exponential regression equation that best fits the data (10, 4) (12, 20) (13, 35) (16, 300), and to estimate the value of y when x = 14.
a. 48.4
b. 73.5
c. 132.3
d. 223.7
1 answer