Chapter 6.4, Problem 8E

To determine

To find: The equation for the curve that best fits the data.

Answer to Problem 8E

The equation for the curve that best fits the data is $E=-0\cdot 001x^2+0\cdot 014x+0\cdot 9678$ .

Explanation of Solution

Given information:

The giventable is shown in figure (1).

  

Figure (1)

Calculation:

The graph is obtained by using $\text{Ti}-83$ calculator.

Press $STAT$ , select edit option and enter the $x$ and $y$ values as shown in the display.

  

Press $STAT$ , select CALC option and select LinReg and press enter as shown the display.

  

In the display screen, Press enter to get the linear equation as shown in the display below.

  

Therefore, the model could be expressed with an exponential function of the form as.

  $y=ax+b$

The exponential model is.

  $E=-0\cdot 0000888x+1\cdot 0006$

Now, press $Y=$ and enter the function, display is shown below.

  

Press $GRAPH$ key to trace the graph as.

  

Press $STAT$ , select CALC option and select QuadReg and press enter as shown the display.

  

In display screen, press enter to get the quadratic equation as shown in the display.

  

Therefore, the model could be expressed with a quadratic function.

The quadratic model is.

  $E=-0\cdot 001x^2+0\cdot 014x+0\cdot 9678$

Now, press $Y=$ and enter the function, display is shown below.

  

Press $GRAPH$ key to trace the graph as.

  

Press $STAT$ , select CALC option and select QuadReg and press enter as shown the display.

  

In display screen, press enter to get the quadratic equation as shown in the display.

  

Therefore, the model could be expressed with a cubic of the form as shown.

The cubic model is.

  $E=6\cdot 5x^3-0\cdot 001x^2+0\cdot 015x+0\cdot 967$

Now, press $Y=$ and enter the function, display is shown below.

  

Press $GRAPH$ key to trace the graph as.

  

From the above graph, quadratic equation suits the model well because the graph is closed to the data. Hence, the equation of the curve for best fit is.

  $E=-0\cdot 001x^2+0\cdot 014x+0\cdot 9678$

Therefore,the equation for the curve that best fits the data is $E=-0\cdot 001x^2+0\cdot 014x+0\cdot 9678$ .