Chapter 4.7, Problem 4MRPS

Solution

To find: Which model fits the data well, the exponential or the power model?

Power model

Given:

The data pairs $\left(7,2562\right),\left(8,2632\right),\left(9,2691\right),\left(10,2747\right),\left(11,2782\right)$.

Explanation:

Use the calculator to create the $\left(x,\ln y\right)$ table.

$x$	$7$	$8$	$9$	$10$	$11$
$\ln y$	$7.848$	$7.875$	$7.898$	$7.918$	$7.931$

The following graph has been obtained using the data of $\left(x,\ln y\right)$ table.

  

Again, use the calculator to create the table of $\left(\ln x,lny\right)$.

$\ln x$	$1.946$	$2.079$	$2.197$	$2.302$	$2.398$
$\ln y$	$7.848$	$7.875$	$7.898$	$7.918$	$7.931$

The following graph has been obtained using the data of $\left(\ln x,lny\right)$ table.

  

The graph of $\left(\ln x,lny\right)$ table seems to be more linear and fits the data well compared to the graph of $\left(x,\ln y\right)$ table. So, it can be concluded that the power model fits the data well.

Conclusion:

The power model fits the data well.