Which equation best represents this graph? A - HSC - SSCE Mathematics Extension 1 - Question 7 - 2018 - Paper 1

To determine which equation best represents the graph, we analyze its asymptotic behavior, initial conditions, and maximum value. The graph appears to approach a horizontal asymptote as time increases.

1. Identify Initial Condition:
   • At time $t=0$, the function should accurately represent the value shown on the graph.
2. Asymptotic Behavior:
   • The highest value the graph approaches (as $t$ approaches infinity) gives an indication of the parameters in the equation.

After examining the options, we find:

• Option C: $P(t) = 3000 + 1500e^{-kt}$ predicts initial growth from a value of 3000, aligning with the graph approach. Thus, this set-up looks plausible.