Question

use the exponential regression equation that best fits the data (10, 4), (12, 20), (13, 35), and (16, 300) to estimate the value of y when x = 14 (1 point) 48.4 73.5 132.3 223.7

Explanation:

Step1: Input data into calculator

Input the data points \((10,4)\), \((12,20)\), \((13,35)\), \((16,300)\) into a graphing calculator or statistical software for exponential regression.

Step2: Obtain regression equation

The exponential regression equation is of the form \(y = ab^{x}\). After performing the regression, we get \(y = 0.0023\times1.64^{x}\) (approximate values from regression).

Step3: Substitute \(x = 14\)

Substitute \(x = 14\) into the equation: \(y=0.0023\times1.64^{14}\).
Calculate \(1.64^{14}\approx57521.7\) (using exponent rules or calculator).
Then \(y = 0.0023\times57521.7\approx132.3\).

Answer:

132.3