Math Question Need Help Please

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