Beth has a rectangular yard that measures 12 feet by 18 ft. she wants to put a fence along the diagonal of the yard. to the nearest tenth, how many feet long will the fence be?

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.