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Answer:
X-intercept = -3 and y-intercept = 6
Step-by-step explanation:
We can start off by isolating the y term. To do that, we must add 2y to both sides to get
Now, we must add 12 to both sides and the y term will be all alone on the right side:
Now, to have only y on the right side, we must divide by 2 to get:
In slope-intercept form, b is the y-intercept, and 'b' in this equation is 6. We have our y-intercept.
To find our x-intercept, y must be equal to zero. We can plug in that value for y and solve for x:
We can start off by subtracting 6 from both sides to get:
We can then divide both sides to get when y is equal to 0. Thus, we have our x-intercept.
<u>Finding the Decay constant(λ):</u>
λ = 0.693 / (half-life)
we are given that the half-life is 36 hours
λ = 0.693 / (36)
λ = 0.01925 /hour
<u>Time taken for 87% decay:</u>
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
<em>Replacing the values in the equation: </em>
<em /><em />
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t = 7.18 hours
<em>We used 'hours' as the unit because the unit of the decay constant is '/hour'</em>
Therefore, the drug will decay to 87% of initial dosage after 7.18 hours