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?

Question

A. After 2 hours

B. After 45 hours

C. After 3 hours

D. After 15 hours

Answer 1

To determine when Frederick would have more Pokémon than Fabricio, we need to compare their results.

For Frederick, the graph shows his results increasing at a constant rate of 5 Pokémon per hour. So, after 1 hour he would have 5 Pokémon, after 2 hours he would have 10 Pokémon, after 3 hours he would have 15 Pokémon, and so on.

For Fabricio, the results of the function f(t)=15t indicate that he would have 15 Pokémon after 1 hour, 30 Pokémon after 2 hours, 45 Pokémon after 3 hours, and so on.

Now we need to find the point at which Frederick's number of Pokémon surpasses Fabricio's.

From the graph, we can see that Frederick will have more Pokémon than Fabricio after 3 hours, with Frederick having 15 Pokémon and Fabricio having 45 Pokémon.

Therefore, the answer is:

C. After 3 hours