The Board shall render a written decision or, when no decision is called for, make written findings on an application within 45 days of the last hearing thereon. Each decision shall be accompanied by findings of fact and conclusions based thereon, together with the reasons therefor. Conclusions based on any provisions of any statute, ordinance, rule or regulation shall contain a reference to the provision relied on and the reasons why the conclusion is deemed appropriate in light of the facts found. Where the Board has power to render a decision and fails to do so within the forty-five-day period above prescribed, the decision shall be deemed to have been rendered in favor of the applicant, unless the applicant agrees in writing to extend the period allowed for decision.