A quantity with an initial value of 8500 decays exponentially at a rate such that the

quantity cuts in half every 5 decades. What is the value of the quantity after 97 years,

to the nearest hundredth?

And we can divide both sides by 8500 and we got:

And we can solve for k using natural log

And we have the model give by:

And if we replace t =97 we got:

Step-by-step explanation:

For this case we can use the proportional model given by:

And we can rewrite the expression like this:

If we integrate both sides we got:

If we apply exponentials in both sides we got:

And we can rewrite the expression like this:

Where P represent the population and t the time in years since the starting value

For this case we have that

And after t = 5*10 = 50 years the value is the half or 8500/2 = 4250

So we can use this condition and we have:

And we can divide both sides by 8500 and we got:

And we can solve for k using natural log

And we have the model given by:

And if we replace t =97 we got:

answer: 1,380

step-by-step explanation:

1: you turn %15 into a decimal by moving the decimal point two places to the left.

2: and then you multiply .15 by 1,200 , which will get you 180.00

3: from there you will add 180 to 1,200

4: which will get you 1,380

hope it *im kind of slow so idk if my answer is right*

b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5