The population of a herd of deer is modeled by
P(t) =4000 + 500sin(2πt - π/2)
where t is measured in years since Jan. 1

A) How does this population vary with time? sketch thegraph of P(t) for one year.
B) Use the graph to decide when in the yr the populationis a maximum. What is the maximum? Is there a minimum? If so,when?
C) Use the graph to decide when the population isgrowing fastest. When is it decreasing fastest?
D) Estimate roughly how fast the population is changingon the first of July.

Question

The population of a herd of deer is modeled by
P(t) =4000 + 500sin(2πt - π/2)
where t is measured in years since Jan. 1

A)  How does this population vary with time? sketch thegraph of P(t) for one year.
B)  Use the graph to decide when in the yr the populationis a maximum. What is the maximum? Is there a minimum? If so,when?
C)  Use the graph to decide when the population isgrowing fastest. When is it decreasing fastest?
D)  Estimate roughly how fast the population is changingon the first of July.

anonymous · Answer

**See attached graph**

A)  I'd say it varies by 1000 from 3500 to 4500 throughout the year.
B)  Maximum on or about June 1 at 4500, a minimum on or about Jan 1 at 3500.  
C)  The population seems to be growing fastest in mid-March and decreasing fastest mid-   
      August. 
D)  ~(-100) deer/month.