Problema Solution
A loptop computer loses 5% of its value each month after it is purchased. it was purchased for $6000.write a function for its value as a function of time.
a) what is the value of the laptop after 3 month?
b) In which month after it is purchased does the laptop's worth fall below $2000?
Answer provided by our tutors
let 't' represent the time in months after the computer is purchased
f(t) = 6,000(1 - 0.05)^t
a) what is the value of the laptop after 3 month?
t = 3 months
f(3) = 6,000(1 - 0.05)^3
f(3) = $5,144.25
the value of the laptop after 3 months is $5,144.25.
b) In which month after it is purchased does the laptop's worth fall below $2000?
we need to find t such that f(t)<2000 that is
6000(1 - 0.05)^t < 2000
t > 21.4
click here to see the step by step solution of the inequality:
for t = 22 months we have
f(22) = 6000(1 - 0.05)^22
f(22) = $1,941.20 < $20000
for t = 21 moths we have
f(21) = 6000(1 - 0.05)^21
f(22) = $2,043.37 > $20000
22 moths after the purchase the computer is worth less than $2,000.