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Three Political Parties


The graph below shows the rates at which three political parties were registering voters in a small community, as measured in people per week, during a time period of the 20 weeks preceding the election. The three political parties are the Republican Party (graphed by $R(t)$), the Democratic Party (graphed by $D(t)$), and the Constitutional Conservative Party (graphed by $C(t)$).

At the beginning of the 20 week time period graphed below, the Republican Party already had 120 registered voters, the Democratic Party already had 165 registered voters, and the Constitutional Conservative Party already had 72 registered voters.

Part 1:
For approximately how many weeks did the Democratic Party register new voters at a faster rate than the Republican Party?

Part 2:
Approximately how many voters did the Democratic Party have registered altogether by the end of the 20 week period?

Part 3:
Estimate the rate at which the Republican Party’s registration rate is increasing between week 12 and week 16, as measured in people per week, per week.