A thief steals a number of plants from a nursery. On the way out, the thief meets three security guards, one after another. To each security guard, the thief is forced to give one-half the plants that he still has, plus 2 more. Finally, the thief leaves the nursery with 1 lone plant.

How many plants were originally stolen?

To receive full credit:

Develop a model to show a general solution. Use the model to show the number of plants originally stolen if the thief has x plants left. Test your model with several example values.

This problem was due in Discussion Board 2 The solution is posted to Blackboard in the Math Resources / Help tab. I will also post a video explaining the solution.

New Problem from Inverse Functions Section 2.7:

Using the original Plants and Guards problem (above), evaluate the solution from an inverse function perspective. Develop a model that shows the number of plants remaining as a function of the number originally stolen.

In the original problem, you determined the number of plants stolen as a function of the number remaining. In this problem determine the number of plants remaining as a function of the number stolen. This approach will allow the thief to be more proactive in determining the number that must be stolen in order to have a certain desired number of plants remaining.

To receive full credit:

Develop a model to show a general solution. Use the model to show the number of plants remaining based on the number originally stolen. Test your model with several example values.

Please help!