A sample of a radioactive substance has an initial mass of 58.7 . This substance follows a continuous exponential decay model and has a half-life of 5 hours.

Question

(a)Let t

 be the time (in hours) since the start of the experiment, and let y

 be the amount of the substance at time t

.

Write a formula relating 

y

 to t.

y=__ e^__(t)

.

Use exact expressions to fill in the missing parts of the formula.

Do not use approximations.

b)How much will be present in 8

 hours?

Do not round any intermediate computations, and round your answer to the nearest tenth.

Answer 1

(a) Exponential decay model: y = y₀e^rt. Now if t = 5 hours then y = y₀/2. So, 1/2 = e^5r, r = ln(1/2)/5

Now our model is y = 58.7y₀e ^(ln(1/2)/5)t.

(b) if t = 8 h y = 58.7e^{- (ln(1/2)/5)·8} ≈ 19.364