Chapter 11.7, Problem 22E

(a)

To determine

To explain:

The data by using a graphing calculator to perform exponential regression.

Answer to Problem 22E

  $y=-826.4217+520.4168\ln x$

Explanation of Solution

Given:

The data of number of the amount.

Concept used:

Formula:

The equation is

  $y=a\times b^x$

Calculation:

The table is

$x$	$-5$	$-4$	$-3$	$-2$	$-1$	$0$	$1$	$2$
$y$	$2.01$	$2.02$	$2.06$	$2.15$	$2.38$	$3$	$4.6$	$8.76$

The data is modeled with an exponential function.

The points approach a horizontal asymptote at $y=2$ .

So, the subtracting from each value before a calculator performed by exponential expression.

Exponential functions is horizontal asymptotes.

But logarithmic functions is not horizontal asymptotes.

(b)

To determine

To find:

The equation in terms of $x$ for the given data.

Answer to Problem 22E

  $y=2+1.0003{\left(2.5710\right)}^x$

Explanation of Solution

Given:

The data of number of the amount.

Concept used:

Formula:

The equation is

  $a^x=e^{\left(\ln a\right)x}$

Calculation:

The table is

$x$	$-5$	$-4$	$-3$	$-2$	$-1$	$0$	$1$	$2$
$y$	$2.01$	$2.02$	$2.06$	$2.15$	$2.38$	$3$	$4.6$	$8.76$

  $a^x=e^{\left(\ln a\right)x}\mathrm{....................}\left(1\right)$

From equation (1)

  $\begin{array}{l}y=c{x}^a\\ \ln y=\ln {\left(cx\right)}^a\\ \ln y=\ln \left(c\right)+\ln {\left(x\right)}^a\\ \ln y=\ln \left(c\right)+a\ln \left(x\right)\\ y=2+1.0003{\left(2.5710\right)}^x\end{array}$

Therefore, the linear function is $y=2+1.0003{\left(2.5710\right)}^x$