Answer:
268 mg
Step-by-step explanation:
Let A₀ = the original amount of caffeine
The amount remaining after one half-life is ½A₀.
After two half-lives, the amount remaining is ½ ×½A₀ = (½)²A₀.
After three half-lives, the amount remaining is ½ ×(½)²A₀ = (½)³A₀.
We can write a general formula for the amount remaining:
A =A₀(½)ⁿ
where n is the number of half-lives
.
n = t/t_½
Data:
A₀ = 800 mg
t₁ = 10 a.m.
t₂ = 7 p.m.
t_½ = 5.7 h
Calculations:
(a) Calculate t
t = t₂ - t₁ = 7 p.m. - 10 a.m. = 19:00 - 10:00 = 9:00 = 9.00 h
(b) Calculate n
n = 9.00/5.7 = 1.58
(b) Calculate A
A = 800 × (½)^1.58 = 800 × 0.334 = 268 mg
You will still have 268 mg of caffeine in your body at 10 p.m.
First is yes
Second is no
Third is no
Fourth is no
Answer: 42/12 or 3.5
Step-by-step explanation:
5(6)/3(-4)= -30/12
-30/12 + 6 or -30/12 + 72/12 = 42/12 or 3.5
Solve equation [1] for the variable u
[1] u = v
// Plug this in for variable u in equation [2]
[2] 8•(v ) - 4v = -32
[2] 4v = -32
// Solve equation [2] for the variable v
[2] 4v = - 32
[2] v = - 8
// By now we know this much :
u = v
v = -8
// Use the v value to solve for u
u = (-8) = -8
Solution : {u , v } = { -8,-8}
since for the bank purposes, there are 360 days in a year, then 270 days is 270/360 years, or namely 3/4 years.
