The half life of a certain tranquilizer in the bloodstream is 36 hours. How long will it take for the drug to decay to 87% of the original dose? Use the exponential decay model to solve.

Finding the Decay constant(λ):

λ = 0.693 / (half-life)

we are given that the half-life is 36 hours

λ = 0.693 / (36)

λ = 0.01925 /hour

Time taken for 87% decay:

Since decay is first-order, we will use the formula:

Where A₀ is the initial amount and A is the final amount

Let the initial amount be 100 mg,

the final amount will be 87% of 100

Final amount = 100*87/100 = 87 mg

Replacing the values in the equation:

t = 7.18 hours

We used 'hours' as the unit because the unit of the decay constant is '/hour'

Therefore, the drug will decay to 87% of initial dosage after 7.18 hours

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation: