# math

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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 -

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 -

can u do a more simpler way...we never learnt log yet..

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