Question

Ryan bought a new computer for $2,100. The value of the computer decreases by 50% each year. When will the

Answer 1

Answer:

After 2.80 years the price drops to 300 $

Step-by-step explanation:

Ryan bought a new computer for $2,100.

Price of computer = 2100 $

The value of the computer decreases by 50% each year.

Let p(n) be the price of computer after n years.

$\texttt{Price of computer after 1 year =}2100-\frac{50}{100}\times 2100=0.50^1\times 2100\ \\\\\texttt{Price of computer after 2 years =}0.50^2\times 2100\ \\\\\texttt{Price of computer after 3 years =}0.50^3\times 2100\ \\\\\texttt{Price of computer after n years =}0.50^n\times 2100$

Now we need to find n when price is 300 $.

              0.50ⁿ x 2100 = 300

                 0.50ⁿ = 0.143

                 n log (0.5) = log 0.143

                  n x -0.301 = -0.845

                  n = 2.80

After 2.80 years the price drops to 300 $