The amount y ( in grams) of a radioactive isotope phosphorus-32 remaining after t days is y=a(0.5)^t/14, where a is the initial amount (in grams) what percent of the phosphorus-32 decays each day

Step-by-step explanation:

The way I figured this out is to just pick some starting values for the grams of this element and plug them into the formula using t = 1 day and seeing how much is left.  I chose 2 different starting amounts and came up with the same percentage each time, so it must be correct!  Here's what I did:

First I chose a starting amount, a, of 10 grams.  Plugging into the formula:

and got that the amount LEFT was 9.5 grams

Then I chose a starting amount, a, of 20 grams.  Plugging into the formula:

and got that the amount LEFT was 19 grams.

I then asked the algebraic question,"What percent of 10 is 9.5?" which translates to

x% * 10 = 9.5 and

x = 95%  (that's the amount left as a percentage).

and

x% * 20 = 19 and

x = 95%

Since both of those came out the same, that tells me that after 1 day there is still 95% of the element remaining, so 5% decays each day.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet