Question

Compounds A and B are used in an experiment. The equation A=30,000(12)t represents the remaining amount of compound A, in milligrams, after t seconds. The table shows the remaining amount of compound B. Time (sec) mg of B (1) 12,000 (2) 6,000 (3) 3,000 What is the positive difference in the initial amount of each compound? Enter your answer in the box.

Answer 1

We are given two compounds A and B, and their rate of consumption.

We are supposed to find the initial amount of each compound.

We have, Amount of compound A left after t seconds = 30000(12) t

It is a linear function.

After 1 sec, amount of A present = 30000(12)(1) = 360000

After 2 sec, amount of A present = 30000(12)(2) = 720000

Increase in amount of compound A in 1 sec = 720000 - 360000 = 360000

Amount B after 1 sec = 12000

Amount of B after 2 sec = 6000

Amount of B after 3 sec = 3000

We see that each second, the amount of B is reducing by half.

So, during the experiment, compound B is consumed to produce compound A.

Initial amount of compound A = 0 mg

Initial amount of compound B = 2* 12000 =24000 mg

Answer 2

Hence, the difference in initial amount is:

6000 mg

Explanation:

• The equation A=30,000(12)^t represents the remaining amount of compound A, in milligrams, after t seconds.

• The table shows the remaining amount of compound B.

Time (sec) mg of B

1 12,000

2 6,000

3 3,000

Hence, the equation for B could be given as:

`B(t)=24000* ((1)/(2))^t`

Now , the initial amount of compound A and B are the amount when t=0.

Hence,

A(0)=30000

Similarly,

B(0)=24000

Hence, the difference in the initial amount is given as:

`=A(0)-B(0)\\\\=30000-24000\\\\=6000mg`

Hence, the difference in initial amount is:

6000 mg