Financial Mathematics

Question

Gabriella purchases a new car. The car's value in dollars, V, is modelled by the function  V(t) = 12870 - k(1.1)^t , t ≥ 0

 

t- the number of years since the car was purchased 

k - constant

k = 3080

 

V(2) = 12870 - 3080 (1.1)²

 

-> This model is defined for 0≤t≤n. At n years the car's value will be zero dollars

 

a) find the value of n

Answer 1

V(n) = 12870 - 3080(1.1)ⁿ = 0

 

12870 = 3080(1.1)ⁿ

 

12870/3080 = (1.1)ⁿ

 

 log (12870/3080) = n log(1.1)

 

n = 1og(12870/3080)/log(1.1)

 

I will leave the arithmetic to you.  You can look up the logs in a log table or most spreadsheet programs have the log function built in and probably your graphing calculator does also.