answer each question

Question

1. Production is related to man power according to the relation: P=15(4)2m-3

 

 What is the production number with 5 men on the line?

 

2. Barry has 300g of a radioactive iodine with a half life of 5 hours. How long will it take for him to have less than 5 grams?   

Answer 1

1. You would just plug in m=5 into the P function.

 

 

2. Exponential decay equation is:

 

A = A₀ * (1 - r)^t

 

Where:

 

A = Ending (final) Value

A₀ = Starting (initial) value

r = rate of decay

t = number of intervals (or amount of time)

 

So if we want to know something about half-life, that means the ratio (A/A₀) = 1/2 (since we end with half as much as we began with) after 5 hours (at t=5).

 

Thus:

 

1/2 = (1-r)⁵

 

(1/2)^1/5 = 1 - r

 

r = 1 - (1/2)^1/5

 

r = 0.1294

 

Now we can use r (the rate of decay) and A₀ = 300g to see at what point in time we have 5g.

 

So:

 

5 = 300*(1-0.1294)^t

 

1/60 = (0.8706)^t

 

log(1/60) = t*log(0.8706)

 

t = log(1/60)/log(0.8706) = 29.5345

 

This means that after about 29.5 hours, Barry will have less than 5g of the radioactive iodine.