Tangent Approximations Word Problem

Question

We are modelling the value of a collectible coin using V(t) = 240(1+t)^1/3, where t is the number of years that have elapsed from the present day. Approximate how much value the coin accumulates from year t=7 to year t=8.

Answer 1

v(t)=240(1+t)^1/3

v'(t)=80/(1+t)^2/3

Tangent linear approximation:

L(t) = v(a)+v'(a)(t-a)

Let a = 7

L(t)=480+20(t-7)

L(8)=500

L(7)=480

Approximate accumulation from year 7 to year 8

L(8)-L(7) = 20

Exact accumulation from year 7 to year 8

v(8)-v(7)= 499.22-480 = 19.22