A coin sold for $252 in 1980 and was sold again in 1987 for $439. Assume that th

Question

A coin sold for $252 in 1980 and was sold again in 1987 for $439. Assume that the growth in the value V of the collector's item was exponential. a) Find the value k of the exponential growth rate. Assume Vo252. (Round to the nearest thousandth.) b) Find the exponential growth function in terms of t, where t is the number of years since 1980. c) Estimate the value of the coin in 2010. (Round to the nearest dollar.) d) What is the doubling time for the value of the coin to the nearest tenth of a year? years (Round to the nearest tenth.)

Explanation / Answer

Vo = 252

V = 439

439 = 252 ( e^7k )

439 / 252 = e^7k

k = .079

b)  exponential growth function is

V(t) = 252 e^.079t

c) value of coin in 2010 is

V = 252 e^.079(20)

value = $1223

d) doubling time

2Vo = Vo e^.079t

ln 2 = .079t

t = 8.8 years

e) 2981 = 252 e^.079t

2981/ 252 = e^.079t

t = 31.3 years

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