A doll sold for $219 in 1973 and was sold again in 1990 for $493. Assume that th

Question

A doll sold for $219 in 1973 and was sold again in 1990 for $493. Assume that the growth in the value V of the collector's item was exponential. Find the value k of the exponential growth rate. Assume V_0 = 219 k = Find the exponential growth function in terms of t, where t is the number of years since 1978. V(t) = Estimate the value of the doll in 2010. $ What is the doubling time for the value of the doll to the nearest tenth of a year? Find the amount of time after which the value of the doll will be $2663.

Explanation / Answer

Sold in 1978 ----$ 219

Sold in 1990 ---- $ 493

Exponential growth: V(t) = Vo(k)^t    wher k is the growth factor t is no. of years and yo is the intial price

493 = 219 (k)^12

taking natural log of both sides:

(493/219) =k^12

a) k= 1.069

b) V(t) = 219(1.069)^t

c) in 2010 :

V(2010) = 219(1.069)^22 = $950.503

e) V(t) = $2663

2663 = 216(1.069)^t

12.3287 = (1.069)^t

taking natural log of both sides:

ln12.3287/ln1.069 =t

t= 37.64 = 38 years

So, i.e 2016

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