To find when Frederick would have more Pokémon than Fabricio, we need to set up an inequality using their results.
Frederick's results can be represented as:
y = 5x^2 - 2x
Fabricio's results can be represented as:
f(t) = 15t
To find when Frederick would have more Pokémon than Fabricio, we need to find the time t when the number of Pokémon Frederick has (5t^2 - 2t) is greater than the number of Pokémon Fabricio has (15t):
5t^2 - 2t > 15t
Rearranging the inequality:
5t^2 - 17t > 0
Factoring out t:
t(5t - 17) > 0
Setting each factor equal to zero to find the critical points:
t = 0 or 5t - 17 = 0
t = 0 or t = 3.4
Since the time t must be greater than 0, we choose the solution t = 3.4. Therefore, after 3.4 hours, Frederick would have more Pokémon than Fabricio.
Frederick and Fabricio enjoy catching Pokémon every day. They have developed different techniques of catching as many Pokémon as possible in an hour. Frederick represented the results of his catching techniques in the graph below, where the x-axis represents the time in hours and the y-axis represents the number of Pokémon in his pokeballs, while Fabricio decided to represent his results as the function f(t)=15t. After how many hours would Frederick have more Pokémon than Fabricio?
1 answer
1 answer