The decay of 742 mg of an isotope is described by the function A(t)= 742e-0.03t, where t is time in years. Find the amount left after 84 years. Round your answer to the nearest mg.

I am really confused.

Question

The decay of 742 mg of an isotope is described by the function A(t)= 742e-0.03t, where t is time in years. Find the amount left after 84 years. Round your answer to the nearest mg.

I am really confused.

wolf1728 · Answer

I don't think that formula is written correctly.

naveenbhatia1312 · Answer

Thats how it was exactly stated

wolf1728 · Answer

I think it should something like
Amount Remaining = 742 e ^ (half-life)
Are you sure there isn't an exponent in there?

naveenbhatia1312 · Answer

the exponent is the -0.03

wolf1728 · Answer

If it is an exponent then it should be written something like:
742e^(-.03t)

unklerhaukus · Answer

$$A(t)= 742e^{-0.03t}$$

wolf1728 · Answer

The typical half life formula is
Amount Remaining = Beginning Amount * e^(-.03t)

unklerhaukus · Answer

$$A(84)= 742e^{-0.03\times84}$$

wolf1728 · Answer

Okay Uncle - you are familiar with these half life problems

anonymous · Answer

I don't think it's half life. Its just an exponential decay question

unklerhaukus · Answer

it's not the half life, because the  base of the exponent is not 2, it is e

anonymous · Answer

e is a natural number

wolf1728 · Answer

yes it is 2.718281828.....

unklerhaukus · Answer

here we have the exponential decay constant $\lambda =  0.03\,/\text{yr}$

wolf1728 · Answer

I guess I should have said an "exponential decay" problem

unklerhaukus · Answer

I am familiar with these problems.

wolf1728 · Answer

I'm familiar with these problems too - but I like it when they are stated in English. Heck, I wrote a calculator for it: http://www.1728.org/halflife.htm

wolf1728 · Answer

So I guess the .03 is the radioactive decay constant

wolf1728 · Answer

jhonyy99
Any thoughts on this?

jhonyy9 · Answer

....is right how ,,Uncle" have said - sure !!!