Chapter 4, Problem 3RE

To determine

Find the indicated values of the exponential function.

Answer to Problem 3RE

  $\boxed{11.954}$ , $\boxed{2.989}$ , $\boxed{2.518}$

Explanation of Solution

Given information:

Use a calculator to find the indicated values of the exponential function, correct to three decimal places.

  $g\left(x\right)=4\cdot {\left(\frac{2}{3}\right)}^{x-2},g\left(-0\cdot 7\right),g\left(e\right),g\left(\pi \right)$

Calculation:

Use a calculator to find the indicated values of the exponential function, correct to three decimal places.

  $\begin{array}{l}g\left(x\right)=4\cdot {\left(\frac{2}{3}\right)}^{x-2}\\ for\\ g\left(-0\cdot 7\right)=4\cdot {\left(\frac{2}{3}\right)}^{\left(-0.7-2\right)}\\ =4\cdot {\left(\frac{2}{3}\right)}^{\left(-2.7\right)}\\ =4\times {\left(0.66666666\right)}^{\left(-2.7\right)}\\ =\frac{4}{0.334621314}\\ =4\times 2.98845279\\ =11.95381116\\ \approx 11.954\end{array}$

  $\begin{array}{l}g\left(x\right)=4\cdot {\left(\frac{2}{3}\right)}^{x-2}\\ for\\ g\left(e\right)=4\cdot {\left(\frac{2}{3}\right)}^{\left(e-2\right)}\\ =4\cdot {\left(\frac{2}{3}\right)}^{\left(2.718281828-2.\right)}\\ =4\times {\left(0.66666666\right)}^{\left(0.718281828\right)}\\ =4\times 0.747337626\\ =2.989350506\\ \approx 2.989\end{array}$

  $\begin{array}{l}g\left(x\right)=4\cdot {\left(\frac{2}{3}\right)}^{x-2}\\ for\\ g\left(\pi \right)=4\cdot {\left(\frac{2}{3}\right)}^{\left(\pi -2\right)}\\ =4\times {\left(0.66666666\right)}^{\left(3.141592654-2\right)}\\ =4\times {\left(0.66666666\right)}^{\left(1.141592654\right)}\\ =4\times 0.629470689\\ =2.517882757\\ \approx 2.518\end{array}$

Hence, the solution is $\boxed{11.954}$ , $\boxed{2.989}$ , $\boxed{2.518}$