) (8 pontos )-Faca um ajuste exponencial , utilizando OS dados da tabela , pelo método dos minimos quadrados.

## Step 1: Understanding the Problem<br />### The task is to perform an exponential fit using the least squares method on a given set of data. This involves finding the best-fitting curve of the form $y = ae^{bx}$ that minimizes the sum of the squared differences between the observed values and the values predicted by the model.<br /><br />## Step 2: Transforming the Exponential Model<br />### To apply the least squares method, we first linearize the exponential model. We start with the equation $y = ae^{bx}$. Taking the natural logarithm of both sides gives $\ln(y) = \ln(a) + bx$. Let $Y = \ln(y)$ and $A = \ln(a)$. The equation becomes $Y = A + bx$, which is a linear equation in terms of $Y$ and $x$.<br /><br />## Step 3: Applying the Least Squares Method<br />### With the transformed linear equation $Y = A + bx$, we can use the least squares method to find the best-fitting line. This involves calculating the slope $b$ and intercept $A$ using the formulas:<br />\[<br />b = \frac{n(\sum x_i Y_i) - (\sum x_i)(\sum Y_i)}{n(\sum x_i^2) - (\sum x_i)^2}<br />\]<br />\[<br />A = \frac{\sum Y_i - b(\sum x_i)}{n}<br />\]<br />where $n$ is the number of data points, $x_i$ are the independent variable values, and $Y_i = \ln(y_i)$ are the transformed dependent variable values.<br /><br />## Step 4: Converting Back to the Exponential Model<br />### Once we have $A$ and $b$, we convert back to the original exponential model. Since $A = \ln(a)$, we find $a$ by taking the exponential: $a = e^A$. Thus, the best-fitting exponential curve is $y = ae^{bx}$.<br /><br />## Step 5: Calculating the Fit<br />### Substitute the given data into the formulas from Step 3 to calculate $b$ and $A$. Then, compute $a = e^A$ to obtain the parameters of the exponential fit.