Question for Growth Models Homework

Question

A radioactive substance decays exponentially. A scientist begins with 140 milligrams of a radioactive substance. After 16 hours, 70 mg of the substance remains. How many milligrams will remain after 23 hours?

Answer 1

16 hours = the half life

70/140= 1/2=

.5 =e^16r, where r= hourly rate of change

take natural logs of both sides

16r= ln.5

r= ln.5/16

A=140e^23r=140e^23(ln.5)/16, simplify

= about 51.69 milligrams left after 23 hours

140 in 0 hours

70 in 16 hours

35 in 16x2=32 hours

35/2=17.5 in 32x2=64 hours

35+17.5=52.5 in 24 hours

slightly less in 23 hours

51.69 looks about right