The question starts off telling us that a laboratory experiments a quantity of a radioactive isotope, which was placed in a closed container.

Measurements were taken to see how much of the isotope remained after various intervals.

The experimenter did not provide information on the initial mass 0 M of the isotope, but suggested that M and 0 M were related by the decay equation

M = M e−kt where k is the decay constant.

I managed to get(a) asked to transform the equation by taking natural logarithms so that a striaght line graph of the form y=mx+c may be plotted. Also state how y,m and c are related to M, M_0, k and t.

ln(M)=ln(M_0*e^(-kt))

ln(M)=ln(M_0) + lne(^(-kt))

ln(M)=ln(M_0) -kt

so y=lnM

m= -k

x= t

c=lnM0

This is the part i'm stuck on From the equation y=mx+c, I should have InM=-kt+InM_0(b)however in the 2nd question, it asks to use my transformation in part (a) to make a new table of values and plot a graph...

However I'm unsure of how to use the values in the table given in the image, to make a new table. If t(hrs) = 5, initially M(mg) was 21.489. But now I have to make a new table with y=mx+c, and i dunno how to input the values into the equation i just made help in the right direction please?