Question

The relationship between the price (P) in dollars and the supply of aluminum baseball bats (S) in millions is given by the function S(P)=0.122P−4.655. According to this model, what can be inferred about the supply of bats when the price is greater than $20?

1) The supply of bats increases as the price increases.
2) The supply of bats decreases as the price increases.
3) The supply of bats remains constant regardless of the price.
4) The supply of bats is not affected by changes in price.

A) S(P)>0 for P>20
B) S(P)<0 for P>20
C) S(P)=0 for P>20
D) S(P) is constant for P>20

Answer 1

The inferred relationship is that the supply of aluminum baseball bats increases as the price increases for P > $20, which is shown when substituting any value greater than 20 into the function S(P) = 0.122P - 4.655, yielding a positive supply. Option a is the answer.

Step-by-step explanation:

The given function representing the supply of aluminum baseball bats in relation to the price is S(P) = 0.122P - 4.655. To infer about the supply of bats when the price is greater than $20, we need to understand if S(P) would be positive, negative, or zero for P > 20.

By substituting any value of P greater than 20 into the function, one can see that the supply S(P) will always yield a positive result, indicating that the supply of bats increases as the price increases.

This means for P > 20, S(P) will always be greater than zero, aligning with option (A).