Question

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

value drop below $300?

Answer 1

After 2.80 years the price drops to 300 $

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-(50)/(100)* 2100=0.50^1* 2100\$\\\\\texttt{Price of computer after 2 years =}0.50^2* 2100\$\\\\\texttt{Price of computer after 3 years =}0.50^3* 2100\$\\\\\texttt{Price of computer after n years =}0.50^n* 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 $