Question

what is the exponential regression equation for the data set?

x	y
3	44
3	41
5	11
4	22
8	3
11	2

y=(0.68cdot99.07)^x
y = 0.68cdot99.07^x
y = 99.07cdot0.68^x
y = 0.68 + 99.07^x

Explanation:

Step1: Recall exponential regression form

The general form of an exponential regression equation is $y = ab^{x}$, where $a$ and $b$ are constants.

Step2: Analyze the given options

An exponential regression equation has the variable $x$ in the exponent. The equation $y = 0.68\cdot99.07^{x}$ is in the correct form of an exponential - regression equation ($a = 0.68$ and $b=99.07$). The equation $y=(0.68\cdot99.07)^{x}=67.3776^{x}$ is also exponential but the structure is different from the typical $y = ab^{x}$ where $a$ and $b$ are treated separately. The equation $y = 0.68+99.07x$ is a linear equation (not exponential as the variable $x$ is not in the exponent), and $y = 99.07\cdot0.68^{x}$ is also exponential but with different values of $a$ and $b$ compared to what might be obtained from the data - set fitting process.

Answer:

$y = 0.68\cdot99.07^{x}$