Question

given the data set.
perform an exponential regression on the data and give the equation.
remember to check log mode if using desmos.
y = \square (\square )^x round your values to the nearest thousandth

Explanation:

Step1: Recall exponential regression form

The exponential regression model is $y = ab^x$, where $a$ is the initial value and $b$ is the growth factor.

Step2: Input data to regression tool

Use the given $(x,y)$ pairs: $(-3,0.3), (-2,0.7), (-1,1.6), (0,3.1), (1,6.6), (2,15), (3,33), (4,66), (5,140)$ in a calculator/tool with log mode enabled for exponential regression.

Step3: Calculate coefficients

The tool computes $a \approx 3.043$ and $b \approx 2.027$ (rounded to nearest thousandth).

Answer:

$y = 3.043(2.027)^x$