Suppose that researchers arc training a group of 60 dolphins

Suppose that researchers arc training a group of 60 dolphins to communicate with humans. They notice that each week 20% of untrained dolphins become trained, but 10% of trained dolphins revert back to untrained status. Create a model for the situation described above. Begin by using T(n) and U(n) to represent the number of trained and untrained dolphins after n weeks. Use the fact that there are 60 dolphins to write a single DDS for T(n). Determine the analytical solution of the model (you do not need an Excel worksheet; you should be able to write down an explicit formula for your model based on our discussions and derivations in the classroom) Assuming that originally all 60 dolphins were untrained, approximately how many will be trained and how many will be untrained after 6 weeks? Instead of a single DDS for T(n), find a DDS for U(n) to find the solution for T(n). Show that this is the same as the solution you obtained earlier.

Solution

tot_dolphin=60

untrained_dolphin=60

trained=0;

n=per week;

loop

for every n 20% of untrained dolphin become trained

trained=untrained_dolphin / 20%

trained= trained- 10%of trained

end // till trained is not equal to 60