A material decays at a rate of 1.1% per year. If you start with 250 grams of the material, in how many years will there be 100 grams remaining? Round to one decimal place.
What would the equation look like?

Question

A material decays at a rate of 1.1% per year. If you start with 250 grams of the material, in how many years will there be 100 grams remaining? Round to one decimal place.
What would the equation look like?

anonymous · Answer

Is the answer 100=250(98.9)^t?

anonymous · Answer

dm/dt = -0.011 m

m(t) = m(0) exp (-0.011 t)  t in years

get t from solving 
m(t)/m(0) = 100/250  = exp(-0.011 t)

by taking logarithms

anonymous · Answer

Oh okay. So is the answer 100=250(98.9)^t?

anonymous · Answer

ln (100/250) = - 0.011 t
t = [ln (100/250)]/[-0.011] = 83.3 years

anonymous · Answer

But is the equation correct? 100=250(89.9)^t?

anonymous · Answer

eys

anonymous · Answer

on no

anonymous · Answer

to decrease a number  by$1.1\%$ multiply it by $100\%-1.1\%=98.9\%=.989$

anonymous · Answer

so it should be 
$$100=250(.989)^t$$ solve for $t$

anonymous · Answer

work with numbers, not percents

anonymous · Answer

Ohhh okay THANK YOU! Alright so now how do I solve that... I get confused once I am at .4=(.989)^t

anonymous · Answer

@satellite73