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torisob [31]
1 year ago
12

Suppose you and your friends form a band and you want to record a demo. Studio A rents for $75 plus $75 an hour and Studio B

Mathematics
1 answer:
Ganezh [65]1 year ago
7 0

Answer:

Step-by-step explanation:

Studio A rents for $75 plus $75 an hour .

Studio B rents for $150 and $50 an hour.

Let t = the number of hours and c = cost.

Part A

Write a system of equations to represent the cost at each studio.

Studio A: c = 75 +75·t

Studio B: c = 150 +50·t

Part B

Solve the system of equations from Part A. Explain your method.

We solve the system of equation using substitution method, where we substitute c in the first equation with 150 +50t.

150 +50·t = 75 +75·t, subtract 75 and 50t from both sides

   150 -75 = 75t -50t, combine likes terms

           75 = 25t, divide both sides by 25

             3 = t

Now we know that t = 3 so we find c by substituting t with 3 in the second equation.

c = 150 +50·t

c = 150 +50·3

c = 300

The solution of the system of equations is c = 300 and t = 3

Part C

Explain what the solution to the system means in terms of where your band will rent a studio.

The solution of the system of equation tells us that if we rent either studio A or B for 3 hours will pay the same price $300.

The price will be different if we rent studio A then studio B if we rent it for a different amount of time than 3 hours.

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A powerful computer is purchased for $2000, but loses 20% of its value each year. How much will it be worth 4 years from now?
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Answer:

(A)Decay

(b)0.8

(c)First Term

(d)f(t)=2000(0.8)^t

(e)$819.20

Step-by-step explanation:

The exponential function for modelling growth or decay is given as:

A(t)=A_o(1\pm r)^t,

Where:

Plus indicates growth and minus indicates decay.

A_o$ is the Initial Value\\r is the growth/decay rate\\t is the time period

For a powerful computer that was purchased for $2000, but loses 20% of its value each year.

(a)Since it loses value, it is a decay.

(b)Multiplier

Its value decays by 20%.

Therefore, our multiplier(1-r) =(1-20&)=1-0.2

Multiplier =0.8

(c)$2000 is our First term (or Initial Value A_o)

(d)The function for this problem is therefore:

f(t)=f_o(1- r)^t\\f(t)=2000(1- 0.2)^t\\\\f(t)=2000(0.8)^t

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