Question

lists the amount of U.S. cash per capita in circulation as of June 30 in the given year. Use linear approximation to estimate the amount, C(2010), of cash per capita in circulation in the year 2010.

Answer 1

C(2010) = $1312 using linear approximation.

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!!!