A laptop computer is purchased for $3600. Each year, its value is 70% of its value the year before. After how many years will the laptop computer be worth

The problem is asking for the number of years it will take for the laptop's value to depreciate to a certain amount. This is a geometric sequence problem where the initial term (a) is $3600 and the common ratio (r) is 0.70 (70%).

The formula for the nth term of a geometric sequence is:

a_n = a * r^(n-1)

We don't know the final value (a_n) or the number of years (n), so we'll have to solve for n. Let's say we want to find out when the laptop will be worth $100. We can set up the equation like this:

100 = 3600 * 0.70^(n-1)

To solve for n, we'll need to use logarithms. First, divide both sides by 3600:

0.02778 = 0.70^(n-1)

Then, take the natural log (ln) of both sides:

ln(0.02778) = ln(0.70^(n-1))

Using the power rule of logarithms (ln(a^b) = b*ln(a)), we can bring down the n-1:

ln(0.02778) = (n-1) * ln(0.70)

Then, divide by ln(0.70) to solve for n-1:

(n-1) = ln(0.02778) / ln(0.70)

Finally, add 1 to solve for n:

n = ln(0.02778) / ln(0.70) + 1

Using a calculator, we find that n is approximately 16. So, it will take about 16 years for the laptop to be worth $100.