The percentage P of doctors who prescribe a certain new medicine is P(t)= 100(1-e^-0.23t), where t is the time, in months. Requried:
a. Find P(1) and P(6).
b. Find P'(t)
c. How many months will it take for 90% of doctors to prescribe the new medicine?
d. Discuss the meaning of the limit limt P(t).
t→[infinity]

1. The percentage of doctors prescribing the new medication will peak after approximately 4.3 years and then decline.
2. The percentage of doctors prescribing the new medication will approach but not exceed approximately 40%.
3. Eventually, all, or nearly all doctors will prescribe the medication.
4. Eventually, no, or almost no doctors will prescribe the medication.