Answer:
a)
b)
c) For this case we want to find when the quantity is below 25 mg, so we can do this:
We can divide both sided by 250 and we got:
Now we can apply natural log on both sides and we got:
And if we solve for t we got:
So the answer for this case would be 12.358 years after.
Step-by-step explanation:
Part a
For this case we know that the decay rate per year is about 17% or 0.17 in fraction and the initial amount is 250 mg for 2009, we can define the model like this:
Where A represent the amount of the substance in mg, r the decay rate = 0.17 and t the number of years after 2009.
Our model for this case would be:
Part b
For this case we have that t= 2023-2009=14 years, so then we can find the amount of substance like this:
Part c
For this case we want to find when the quantity is below 25 mg, so we can do this:
We can divide both sided by 250 and we got:
Now we can apply natural log on both sides and we got:
And if we solve for t we got:
So the answer for this case would be 12.358 years after.