Problema Solution
The value of a car is appreciating over time. the car was purchased for $5.52 in 1990. if the car is growing in value at a rate of 4% write an equation modeling the value, V(t) in dollars of the car over time, t years after 1990. what is the car valued at today?
Answer provided by our tutors
for t = 0 years, in the year of 1990 the value of the car is:
V(0) = $5.52
for t = 1 years, after 1 year the value will grown by 4% that is
V(1) = V(0) + 0.04V(0) = 1.04V(0)
for t = 2 years we have
V(2) = 1.04V(1) = 1.04^2 V(0)
or in general
V(t) = 1.04^t V(0)
V(t) = 1.04^t * 5.52
today is 2014, t = 2014 - 1990 = 24 years
V(24) = 1.04^24 * V(0)
V(24) = 1.04^24 * 5.52
V(24) = $14.15
the value of the car today is $14.15.