President Carter's popularity has declined to a new low as Americans become increasingly apprehensive about inflation.

About four in 10 Americans (39 percent) say they approve of his handling of the presidency, down nine points from the previous measurement in late March and down 16 point from the first 1978 measurement, taken in early January.

The downtrend in Carter's popularity coincides with the public's growing concern over inflation. As reported earlier, the proportion who believe prices will rise faster than income in the next 12 months has increased today 45 percent in March to 55 percent today. Only small proportions in each survey think income will rise faster than prices.

In addition, 50 percent of Americans feel the economic situation will worsen in the next six months, while only about half as many, 27 percent, think it will improve.

The American people favor far more drastic economic measures than those prescribed by Carter.

A growing number favors wage and price controls, with 50 to 39 percent in support, compared with 44 with to 40 percent two months ago.

As many few favor reducing the budget deficit s favor proposed tax cuts.

By an overwhelming 9 to 1, the public feels that controlling inflation is more important than cutting taxes.

This question was asked to determine the president's popularity.

"Do you approve or disapprove of the way Carter is handling his job as President? "(TABLE) (COLUMN)Approval(COLUMN)Disapproval(COLUMN)No opinion Latest (April 14-17)(COLUMN)39%(COLUMN)46%(COLUMN)15% March 31-April 3(COLUMN)48(COLUMN)39(COLUMN)13 March 10-13(COLUMN)50(COLUMN)35(COLUMN)15 March 3-6(COLUMN)49(COLUMN)33(COLUMN)18 Feb. 24-27(COLUMN)50(COLUMN)33(COLUMN)17 Jan. 20-23(COLUMN)52(COLUMN)28(COLUMN)20 Jan. 6-9(COLUMN)55(COLUMN)27(COLUMN)18(END TABLE)