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Len [333]
3 years ago
5

The pool at "Splash Around" is open for 14 weeks during the summer. You can swim for $6 a session, or you can buy a membership f

or $100 and pay only $4 a session. Which equation would you use to determine how many sessions you must use the pool to justify buying the membership? A) 4x = 100 + 6x B) 6x + 4x = 100 C) 6x = 100 + 4x D) 100 - 4x = 6x
Mathematics
2 answers:
shutvik [7]3 years ago
8 0
C) 6x=100+4x
This is because since you need to justify buying a membership, you would try and equal the prices between not having a membership which is 6x and having a membership which is 100+4x
Yanka [14]3 years ago
7 0

Answer:

C) 6x=100+4x

Step-by-step explanation:

Let the number of sessions be x

Let the total payment be y

Without membership, the equation becomes:

y=6x

With membership, the equation becomes:

y=100+4x

Now to justify, $100, we will equal both to get the number of sessions.

6x=100+4x

=> 2x=100

Dividing both sides by 2;

x = 50

Hence, the right equation is : 6x=100+4x

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<u>Step-by-step explanation:</u>

A = P_o\cdot e^{kt}\\\\\text{First, use the given information to find k:}\\\\\bullet A=\dfrac{1}{2}P_o\\\\\bullet k = unknown\\\\\bullet t=29\text{ years}\\\\\dfrac{1}{2}P_o=P_o\cdot e^{k(29)}\\\\\\\dfrac{1}{2}=e^{k(29)}\qquad divided\ both\ sides\ by\ P_o\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=ln\bigg(e^{k(29)}\bigg)\qquad applied\ ln\ to\ both\ sides\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=29k\qquad simplified-ln\ and\ e\ cancel\ out\\\\\\\dfrac{ln\bigg(\dfrac{1}{2}\bigg)}{29}=k\qquad divided\ 29\ from\ both\ sides\\\\\\-0.0239=k

\text{Now, use the following in the equation to solve for A:}\\\\\bullet A=unknown\\\bullet P_o=500\\\bullet k=-0.0239\\\bullet t=58\text{ years}\\\\A=500\cdot e^{(-0.0239)(58)}\\\\.\quad=500\cdot e^{-1.386}\\\\.\quad=125

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