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

Question

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

Answer 1

### Realize o ajuste exponencial utilizando os dados fornecidos na tabela pelo método dos mínimos quadrados conforme descrito nos passos acima.

Answer 2

## Step 1: Understanding the Problem### 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

that minimizes the sum of the squared differences between the observed values and the values predicted by the model.## Step 2: Transforming the Exponential Model### To apply the least squares method, we first linearize the exponential model. We start with the equation

. Taking the natural logarithm of both sides gives

. Let

and

. The equation becomes

, which is a linear equation in terms of

and

.## Step 3: Applying the Least Squares Method### With the transformed linear equation

, we can use the least squares method to find the best-fitting line. This involves calculating the slope

and intercept

using the formulas:

where

is the number of data points,

are the independent variable values, and

are the transformed dependent variable values.## Step 4: Converting Back to the Exponential Model### Once we have

and

, we convert back to the original exponential model. Since

, we find

by taking the exponential:

. Thus, the best-fitting exponential curve is

.## Step 5: Calculating the Fit### Substitute the given data into the formulas from Step 3 to calculate

and

. Then, compute

to obtain the parameters of the exponential fit.

Question

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

Solution

Resposta

Explicação