"continued to moderate" is correct and can be used in written English.
It is used when one wants to describe a gradual decrease or change in something. For example, "Although the weather had been hot during the first part of the week, temperatures continued to moderate as the week progressed."
Export growth continued to moderate, rising 15.9 percent over levels of a year ago.
The largest banks have continued to moderate the need for significant changes to Dodd-Frank in large part due to their recognition that Dodd-Frank has been successful in reducing systemic risk, which was its primary aim.
"My sister's position has continued to moderate," he said.
WASHINGTON -- Republican presidential nominee Mitt Romney on Tuesday continued to moderate his past positions, this time glossing over his previous support for a tough amendment on contraception policy.
Like the VZ model before it, Holden with the VE have continued to moderate the long-standing tradition of implementing substantial updates marked by the frequent use of new model designations (such and VT, VX, and VY) successively interspersed with "Series II" and occasional "Series III" revisions.
It said the upward trends in charge-offs and bad loans "continue to moderate and credit costs overall remain very manageable".
The emphasis of much of the recent diplomacy has been to get North Korea to continue to moderate its behavior in order to gain access to international aid and investment.
Economists saw signs that the pace of job loss would continue to moderate, not least because most of the effects of the federal stimulus plan have yet to be felt.
As the Roman Catholic church is excluded from official status in Russia, this is an area he must navigate extremely carefully – perhaps by continuing to moderate his own conciliatory instincts.
