If 14 g of a radioactive substance are present initially and 3 years later only 7 g remain, how much of the substance will be present after 4 yr?

5.56 g

We are given;

We need to determine the mass that will be present  after 4 years.

                                  = 4/3

Using the formula;

Therefore;

Remaining mass = 14 g × 0.5^4/3

                            = 5.56 g

Thus, the remaining mass after 4 years will be 5.56 g

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