Compounds a and b are used in an experiment.

the equation y=500(0.5)x

represents the remaining amount of compound a, in grams, after x hours. the table shows the remaining amount of compound b.
time (h) grams of b
1 200
2 100
3 50

what is the positive difference in the initial amount of each compound?

Positive Difference = 100 grams

Step-by-step explanation:

We have two compound A and B

Compound A:

We have to find initial value of compound A. For initial value, we will put x=0 into equation.

Initial amount

Initial amount of compound A = 500 grams

Compound B:

Time (h)           :    1         2        3

Compound B  : 200    100     50

First we have to make the function for compound B.

According to table we can see amount becomes 50% of previous value every hour.

In 1 hour, Compound B = 200 grams

Initial amount should be 50% more than 200.

Initial amount of Compound B = 400 grams

We need to find positive difference of initial amount of compound  A and B

Difference = 500 - 400

Positive Difference = 100 grams

Hence, The positive difference of initial amount of Compound A and Compound B is 100 grams.

where is the page?

step-by-step explanation:

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: