Question

Radioactive decay is the process by which an unstable element transforms into different element, typically releasing energy as it does so. For 500g of a radioactive substance with a half-life of 5.2 hours, the amount remaining is given by the formula M(t)=500(0.5) ^ t/5.2

a) calculate the average rate of change between 8 days and 15 days.
b)calculate the approximate instantaneous rate of change when t=2hours

Answer 1

When you are in caclulus, you will have a much easier and elegant way of doing this.

For now

avgratechange=(rate8 - rate 15)/(8-15)

rate 8=500(1/2)^8 and likewise for the rate15

approximate rate at t=2
(500*(.5)^(2+e)-500(.5)^2)/e
500*(.5)^2 (.5^e -1)/e
now the limit of this as e approaches zero (I leave it to you to prove) will be.
500*.5^2 ln .5

Answer 2

(rate 5+ rate 8) / (15-8) ?
t is measured in hours

Answer 3

So use 8 days * 24 hr/day = 192 hours and 15*24 for 15 days and proceed as advised.

Answer 4

72y2-98