A radioactive substance decays at a continuous rate of 17% per year, and 250 mg of the substance is present in the year 2009.

(a) Write a formula for the amount present, A (in mg), years after 2009.
(b) How many milligrams will be present in the year 2023? Round your answer to three decimal places. In the year 2023 the amount of the substance is +23.1
(c) Estimate when the quantity drops below 25 mg. Round your answer to the nearest integer. mg The quantity drops below 25 mg in the year

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.

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step-by-step explanation:

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