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The analog simulation of an overdamped Brownian particle in a quartic double-well potential driven by an external ͑either Gaussian or dichotomic͒ multiplicative noise is performed with special focus on the phenomenon of resonant activation. Such an effect is shown to occur on increasing the correlation time of the multiplicative noise, while keeping the noise variance constant. The asymptotic behavior of the relevant escape times for large noise correlation time and large variance is also investigated. Simple qualitative arguments are produced to justify the results thus obtained. Furthermore, the traversal barrier, that is the effective barrier at the time the system switches state, is shown to have a minimum for a certain value of the noise correlation time, though not always in coincidence with the relevant resonant activation value. ͓S1063-651X͑96͒05610-3͔PACS number͑s͒: 05.40.ϩj, 82.20.Mj