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If someone may help me with this attached photo below, I’m having problems with this question and it’s taking me a while to solve and I can’t figure it out.
Solution
a) The initial mass would be M0
b) The graph will be a log graph. At t = 0, M = M0, then plot M as a percent of M0 as t increases
c) After 10 years, t = 10
M = M0 x 2-0.0346t
M = M0 x 2-0.0346(10)
M = M0 x 2-0.346
M = M0 x (.7867)
M = .7867M0
So the mass after 10 years is .7867 the initial mass. Therefore the percentage mass lost is (1-.7867), or .2133, which is 21.33% mass lost
d) 10% of the original mass would be .1M0 so we’d use the equation
.1 M0 = M0 x 2-0.0346t
.1 = 2-0.0346t
log (.1) = log (2-0.0346t)
log (.1) = -0.0346t log 2
-1 = -0.0346t (.301)
-1 = – 0.010416t
96= t
So after 96 years, the mass is 10% of the original mass