In a certain chemical reaction, a substance is converted into another substance at a rate proportional to the square of the amount of the first substance present at any time t. Initially (t = 0) 45 g of the first substance was present; 1 hr later, only 10 g of it remained.

Find an expression that gives the amount of the first substance present Q(t) at any time t.

Q(t) = ?

What is the amount present after 2 hr? (Round your answer to two decimal places.)
g

Step-by-step explanation:

Let Q(t) be the first substance at time t. We know that the rate of change is directly proportional to .

Hence we can write it as:

Step 1: Integrating the function to form an equation:

  ----------------------------------------------- equation (1)

Step 2: Substitute the value Q(0) = 45 in equation 1 to find value of C.

---------------------------------------------- equation (2)

Step 3: Substitute the value Q(1) = 10 in equation 2 to find the value of k.

Step 4: Form the equation and simplify it.

Step 5: To find the amount of substance after 2 hours, we substitute the value of t with 2.

The amount of substance after 2 hours is 5.63 grams.

step-by-step explanation:

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step-by-step explanation: