This question involves the half-life formula. In this exercise, we are to give a half-life for an exponentially decaying quantity. Need answer to the following: The half-life of a drug in the bloodstream is 4 hours. By what factor does the concentration of the drug decrease in 24 hours? in 36 hours?
If you want to use the formula...
amount remaining= origamount*e^(-.692t/4)
put in the t, and solve.
Another way is
amountremaining= (1/2)^t/4
when t=24
amountremaining= 1/2^(6)= 1/64 th
To answer this question, we can use the half-life formula for exponential decay:
N(t) = N₀ * (1/2)^(t / t₁/₂)
Where:
N(t) = the quantity at time t
N₀ = the initial quantity
t = the time elapsed
t₁/₂ = the half-life of the substance
In this case, the half-life of the drug is 4 hours. Let's calculate the decrease factor for 24 hours and 36 hours.
For 24 hours:
N(t) = N₀ * (1/2)^(t / t₁/₂)
N(t) = N₀ * (1/2)^(24 / 4)
N(t) = N₀ * (1/2)^6
N(t) = N₀ * (1/64)
The concentration of the drug decreases by a factor of 1/64 in 24 hours.
For 36 hours:
N(t) = N₀ * (1/2)^(t / t₁/₂)
N(t) = N₀ * (1/2)^(36 / 4)
N(t) = N₀ * (1/2)^9
N(t) = N₀ * (1/512)
The concentration of the drug decreases by a factor of 1/512 in 36 hours.
So, the concentration of the drug decreases by a factor of 1/64 in 24 hours and by a factor of 1/512 in 36 hours.