Morgan Kaminski just received a signing bonus of $$3,000,000.$ His plan is to invest this payment in a fund that will earn $6\%,$ compounded annually. $($For calculation purposes, use $5$ decimal places as displayed in the factor table provided.$)$

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$($a$)$

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If Morgan plans to establish the Morgan the Tank Foundation once the fund grows to $$4,510,890,$ how many years until he can establish the foundation?

years