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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

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

Verified Answer :

Edufirst

Attached you will find a file with the answers, including the graph and the table of data.

I used Excel to plot the graph. First you have to create the table of data.

To create the table use:

- a column for the days from 1 to more than 365 (enough to include several years), pass the days to years (dividing by 365)
- in the next column, calculate the function: P(t) =4000 + 500sin(2πt - π/2)

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