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Question

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?

Answer 1

To find out when Frederick would have more Pokémon than Fabricio, we need to compare their results at different time intervals.

Frederick's results can be represented by the graph below. Let's assume Frederick's catching techniques shown in the graph result in the function g(t), where g(t) is the number of Pokémon caught by Frederick at time t.

At t=1 hour, Frederick catches 10 Pokémon.
At t=2 hours, Frederick catches 20 Pokémon.
At t=3 hours, Frederick catches 26 Pokémon.
At t=4 hours, Frederick catches 30 Pokémon.
At t=5 hours, Frederick catches 35 Pokémon.
At t=6 hours, Frederick catches 37 Pokémon.

Fabricio's results are represented by the function f(t) = 15t.

Now, we need to compare Frederick's results with Fabricio's results at each time interval:

At t=1 hour:
g(1) = 10
f(1) = 15
Frederick has fewer Pokémon than Fabricio.

At t=2 hours:
g(2) = 20
f(2) = 30
Frederick has fewer Pokémon than Fabricio.

At t=3 hours:
g(3) = 26
f(3) = 45
Frederick has fewer Pokémon than Fabricio.

At t=4 hours:
g(4) = 30
f(4) = 60
Frederick has fewer Pokémon than Fabricio.

At t=5 hours:
g(5) = 35
f(5) = 75
Frederick has fewer Pokémon than Fabricio.

At t=6 hours:
g(6) = 37
f(6) = 90
Frederick has fewer Pokémon than Fabricio.

So, it is clear that Frederick never has more Pokémon than Fabricio based on their given results.

Answer 2

what about after 15 hours?

Answer 3

Let's calculate the number of Pokémon caught by Frederick after 15 hours using his catching techniques as represented in the graph:

At t=15 hours, the graph does not provide an exact point. However, we can estimate based on the trend shown in the graph.

From t=6 to t=15, Frederick catches an additional approximately 3 Pokémon in each hour.

So, estimating Frederick's catches at 15 hours:
g(15) ≈ g(6) + 3*(15-6)
g(15) ≈ 37 + 27
g(15) ≈ 64

Now, let's calculate the number of Pokémon caught by Fabricio after 15 hours using his function f(t) = 15t:

f(15) = 15*15
f(15) = 225

Comparing the results:
Frederick caught approximately 64 Pokémon after 15 hours.
Fabricio would have caught 225 Pokémon after 15 hours.

Therefore, even after 15 hours, Fabricio would still have more Pokémon than Frederick.