Final answer:
The student's question regarding the increasing value of a Patrick Mahomes rookie card can be modeled with the equation V = 250(1.03)^t, where V represents the future value of the card, and t represents the number of years Mahomes continues to play football.
Step-by-step explanation:
The student is asking for an equation that models the increasing value of a Patrick Mahomes rookie football card. This situation can be represented by an exponential growth equation. The initial value of the card is $250, and it increases by 3% annually as long as Mahomes plays football. To represent this mathematically, we use the formula for exponential growth:
V = P(1 + r)^t
Where:
- V = future value of the card
- P = present (initial) value of the card
- r = annual growth rate (in decimal form)
- t = number of years Mahomes plays
To make this specific to the given situation:
V = 250(1 + 0.03)^t
Thus, V = 250(1.03)^t is the equation Mr. Roach would use to determine the future value of the Patrick Mahomes rookie card.