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During a heat treatment, spherical precipitates of phase form and grow in a matrix of phase. In experiments, we measure the transformed volume fraction, .

During a heat treatment, spherical precipitates of phase form and grow in a matrix of phase. In experiments, we measure the transformed volume fraction, . The following results are obtained: At time t = 0.4 hours, volume fraction of the phase is = 0.2, and for time t = 0.9 hours, the transformed volume fraction is = 0.5. Estimate the time needed to obtain = 0.98. Assume linear particle growth rate, i.e., R(t) t and V(t) t3

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