Evaluating an Exponential Decay Function?

Question

A Radioactive material decays at a rate of 3.6% per year. The amount, y , left after t years can be found by the formula y=yoe -0.0336t. Where y is the original amount <7> and 30 is t. Mt question is I have figured out how to find most of it but the last part is 7e-1.008 I do not know what to do with e to make the final answer. Could someone please help or explain

Answer 1

e^(at), where a is any #, is just 2.718 to the power a*t. e is the natural log, where 10 is the log we use cause our math system is decimal (base 10). Nature works with a base 2.718 (e). So on your calculator..do 2.178..^..(-0.00336*30) or on sci. calcs use e^x (-0.0036*30)

Answer 2

y=yoe -0.0336t.

Let OA = original amount

and FA = final amount

FA =OA (e^(-0.036t))

Divide both sides by OA
e^(-0.036t) = (FA)/(OA)

take the natural logarithm of both sides
(the ln of e^x is x)

-0.036t = ln(FA)/(OA)

t = -ln((FA)/(OA))/0.036
.