Final Answer:
A. The slope of the function is 4.
B. In practical terms, the slope of this function (4) represents the rate at which the number of people in the math club increases per week.
Step-by-step explanation:
The given function is ( P = 4t + 12 ), where ( P ) is the number of people in the math club and ( t ) is the time in weeks since the first of the year.
A. The slope of the function is the coefficient of the variable ( t ) in the equation, which is 4. In mathematical terms, the slope represents the rate of change of the dependent variable ( P ), in this case) with respect to the independent variable ( t ). Therefore, the slope of 4 indicates that for each additional week ( t ), the number of people in the math club (( P )) increases by 4.
B. In practical terms, this means that the math club is gaining 4 new members per week. The initial value of 12 (when ( t = 0 )) accounts for the starting membership, and as each week passes, 4 more members join. The slope reflects the steady growth in the math club's membership. For instance, after 1 week (( t = 1 )), the membership would be
, and after 2 weeks (( t = 2 )), the membership would be
, and so on. The slope provides a practical understanding of the incremental increase in the math club's size over time.