Answer:
C(2010) = $1312 using linear approximation.
Step-by-step explanation:
The full complete question is attached to this solution.
The full table is given as
Year | 1970 | 1980 | 1990 | 2000
Cash |$180 |$262 |$564 | $938
we are told to use linear approximation to obtain C(2010)
Linear approximation, Mathematically, results in
C(2010) = C(2000) + C'(t) [t]
where t = years since 2010 = (Year - 2000)
Linear approximation gives C'(t) as the rate of change of C with time
C'(t) = (ΔC/Δt)
We will be using the latest year for this approximation.
ΔC = C(2000) - C(1990) = 938 - 564 = $374
Δt = 2000 - 1990 = 10
C'(t) = (374/10) = $37.4 per year.
C(2010) = C(2000) + C'(t) [t]
t = 2010 - 2000 = 10
C(2000) = $938
C'(t) = $37.4 per year
C(2010) = 938 + (37.4)(10) = $1312
Hope this Helps!!!
