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: