f(t+1) = 3(t+1)^2 + 5(t+1) + 2
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- 5**Question:** A volcanologist is using a mathematical model to predict lava flow rates from a volcano. If the flow rate \( f(t) \) is given by \( f(t) = 3t^2 + 5t + 2 \), expand the expression for \( f(t+1) \).
- To expand \( f(t+1) \), substitute \( t+1 \) into the function:
- First, expand \( (t+1)^2 \):
- Now substitute back:
- f(t+1) = 3(t^2 + 2t + 1) + 5(t+1) + 2
