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gives the lion population at a certain game reserve years after the reserve was established.What is the best interpretation for the following statement?The value of the derivative of at is equal to .Choose answer:(A) After years, the lion population grows at a rate of lions.(B) After years, the lion population grows at a rate of lions per year.(C) The lion population grows at a rate of lions per years.(D) After years, there were lions in the reserve.
Full solution
Q. gives the lion population at a certain game reserve years after the reserve was established.What is the best interpretation for the following statement?The value of the derivative of at is equal to .Choose answer:(A) After years, the lion population grows at a rate of lions.(B) After years, the lion population grows at a rate of lions per year.(C) The lion population grows at a rate of lions per years.(D) After years, there were lions in the reserve.
- Rate of Change Definition: The derivative of with respect to represents the rate of change of the lion population with respect to time.
- Derivative at : At , the derivative being means that at that specific time, the population is increasing at a rate of lions per year.
- Instantaneous Rate Clarification: This rate of change is an instantaneous rate, not an average over a period of time, so it's per year, not per years.
- Correct Interpretation: Therefore, the correct interpretation of the derivative value is that after years, the lion population grows at a rate of lions per year.
