Reacting with water in an acidic solution at a particular temperature, compound A decomposes into compounds B and C according to the law of uninhibited decay. An initial amount of 0.30 M of compound A decomposes to 0.25 M in 30 minutes. How much of compound A will remain after 3 hours? How long will it take until 0.10 M of compound A remains?

Step-by-step explanation:

We would apply the formula,

A(t) = Aoe^kt

Where

Ao represents the initial concentration of compound A.

k represents the rate of decomposition.

t represents the decomposition time.

A(t) represents the concentration after t hours.

From the information given

Ao = 0.30 M

t = 30 minutes = 0.5 hour

A(0.5) = 0.25 M

Therefore,

0.25 = 0.3e^0.5k

0.25/0.3 = e^0.5k

0.833 = e^0.5k

Taking ln of both sides, it becomes

ln0.833 = ln e^0.5k = 0.5k

k = - 0.1827/0.5

k = -0.3654

The expression becomes

A(t) = 0.35e^-0.3654t

1) When t = 3 hours,

A(3) = 0.35e^-0.3654 × 3

A(3) = 0.35e^- 1.0962

A(3) = 0.117M

2) When A = 0.1, then

0.1 = 0.35e^-0.3654 × t

0.1/0.35 = e^-0.3654t

0.2857 = e^-0.3654t

Taking ln of both sides, it becomes

Ln 0.2857 = - 0.3654t

- 1.2528 = - 0.3654t

t = - 1.2528/- 0.3654

t = 3.43 hours

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step-by-step explanation:

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mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: