Question

ONLY EXERCISE B!

Find the mass that remains after t years.

Step 1

Let y(t) be the mass (in mg) remaining after t years.

Then we know the following.

y(t)	=	y(0)ekt
	=	10    10 · ekt

Step 2

Since the half-life is 30 years, then y(30) = 5  

5

mg.

Step 3

Thus, 5 = 10e^30k, or e^30k = 1/2  

1/2

.

Therefore, k =  

$$−ln(2)30​

    .

Step 4

Now, remembering that

ln(xⁿ) = n ln(x)

and that

e^ln(z) = z,

we havey(t) = 10e^{(t/30)(−ln(2))} =  

$$10·2−(t30​)

    mg.

Exercise (b)

How much of the sample remains after 40 years?

Answer 1

You are very sure the formula you provided is right leave the (*) region.

Do let me know if you have any confusions.

Please upvote. Thank you ?.