Exponential Regression Find Fit

## Description

Here, we will create an exponential regression for the following data set and plot the regression with a scatter plot of the data.

(1)\begin{align} \{ \ (0, 1.0647), \ (1, 1.2189), \ (2, 1.6752), \ (3, 3.3014), \ (4, 8.5549) \ \} \end{align}

Sage has no default model for `find_fit()`, so we must set one with other letters as constants, declaring them with `var()`. In order to perform an exponential regression, the model we pass to `find_fit()` is the standard exponential form, $ae^{bx} + c$. In Sage, we use `exp(x)` to represent $e^x$.

## Sage Cell

#### Code

```
var('a b')
dataset = [ (0, 1.0647), (1, 1.2189), (2, 1.6752), (3, 3.3014), (4, 8.5549) ]
model(x) = a*exp(b*x)
find_fit(dataset, model)
```

```
r(x) = 0.0641*exp(1.1921*x) + 0.9981
p1 = plot(r(x), -1, 5)
p2 = scatter_plot( dataset )
(p1 + p2).show()
```

## Options

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Date: 07 Mar 2019 17:15

Submitted by: Zane Corbiere