Question

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Answer 1

Answer:

The number of players who went on to play professionally at academy A can be represented by an arithmetic sequence because the numbers of players who went on to play professionally in successive years have a common difference of 10.

Step-by-step explanation:

It is given that:

Tow tennis academies each have 120 players.

Also,

• In academy A the number of players increases by 10 players each year.

This means that the function that can be used to model this situation is:

$p(t)=120+10t$

where p(t) is the number of players in academy A in t years.

This means that the number of players are increasing by a constant rate i.e. 10.

Hence, the sequence so formed will be an arithmetic sequence.

with a common difference of 10.

• Also, in academy B the number of players increased by 10% every year.

It could be modeled by the function:

$P(t)=(1.10)^t\times 120$

This means that the number of players are increasing by a multiplicative rate of 1.10 and the increase is exponential.

Also, the sequence so formed will be a geometric sequence and the common ratio is 1.10.

Answer 2

Answer:

Academy A, Arithmetic, and difference makes most sense to me.