A sample of a radioactive isotope had an initial mass of 800 mg in the year 2000 and decays exponentially over time. A measurement in the year 2005 found that the sample's mass had decayed to 190 mg. What would be the expected mass of the sample in the year 2009, to the nearest whole number?

dude thats to long figure it

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4