Chapter 6, Problem 13CT

To determine

To find : how many barrels of oil would you expect to collect after drilling 1000 wells and the inverse function of the equation

Answer to Problem 13CT

Expect to collect $y=39.332$ barrels of oil after drilling 1000 wells and the inverse function is $y=e^{\frac{x+45.381}{12.263}}$

Explanation of Solution

Given information

  $y=12.263\ln x-45.381$

Where $y$ is measured in billions of barrels and $x$ is the numbers of wells drilled.

Calculation :

You would expect to collect barrels of oil after drilling 1000 wells.

  $\begin{array}{l}y=12.263\ln x-45.381\\ y=12.263\ln \left(1000\right)-45.381\\ y=12.263\cdot 6.908-45.381\\ y=84.713-45.381\\ y=39.332\end{array}$

The inverse of the function

  $\begin{array}{l}x=12.263\ln y-45.381\\ 12.263\ln y=x+45.381\\ \ln y=\frac{x+45.381}{12.263}\\ y=e^{\frac{x+45.381}{12.263}}\end{array}$

Hence, expect to collect $y=39.332$ barrels of oil after drilling 1000 wells and the inverse function is $y=e^{\frac{x+45.381}{12.263}}$ .