Posted by **Kristen** on Sunday, June 23, 2013 at 12:30pm.

A researchr assistant made 160mg of a radioactive, and found that there was only 20mg left after 45hours.

a) What is the half-life of this substance?

b) Write a function to represent the amount of substance left after x hours

c) If the researcher kew he needed 100mg of the same substance 12 hours after he was able to make a fresh batch, how much should he initially make?

Please help.i have a feeling that something like this will b on my math exam

Please show some steps so I can understand how u get it.

Thanks a bunch I really appreciate it!:)

- math -
**MathMate**, Sunday, June 23, 2013 at 1:30pm
This is an exponential function of the form

y=ae^x

Substituting x,y values (20,45)into the equation,

20=160*e^(45k)

take logs on both sides and solve for k

k=-(1/45)ln(8)

=-0.04621

So the mathematical model becomes:

y(t)=y0*e^(-0.04621t)

t=time in hours

y0=initial mass

y(t)=mass at time t hours.

Half life (value of t when y(t)/y0=1/2)

is

0.5 = e^(-0.04621t)

Take logs on both sides,

-0.04621t = ln(0.5)

t=15

- math -
**Kristen**, Sunday, June 23, 2013 at 1:50pm
can u do a more simpler way...we never learnt log yet..

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