Answer:
Step-by-step explanation:
a) The equation relating A to the amount left of an initial amount Upper A 0 after time t is
A(t) = A0e^(kt)
b) It is found that 18 lb of A will reduce to 9 lb in 4.2 hr. It means that
A0 = 18
A = 9
t = 4.2
Therefore, substituting into the formula, it becomes
9 = 18e^(4.2k)
9/18 = e^(4.2k)
0.5 = e^(4.2k)
Taking ln of both sides of the equation, it becomes
Ln0.5 = ln e^(4.2k)
- 0.693 = 4.2k
k = - 0.693/4.2
k = - 0.165
The equation becomes
A(t) = 18e^(- 0.165t)
For A = 1(1 lb left), then
1 = 18e^(- 0.165t)
1/18 = e^(- 0.165t)
0.056 = e^(- 0.165t)
Taking ln of both sides, it becomes
Ln0.056 = ln e^(- 0.165t)
- 2.88 = - 0.165t
t = - 2.88/-0.165
t = 17.5 hours
After 17.5 hours, 1 lb would be left
