Updated at 8:43 a.m. ET

Another 3.2 million people filed for unemployment for the first time last week, bringing the total number of jobs lost during the coronavirus crisis in the last seven weeks to at least 33.5 million.

Last week's number was down from the nearly 3.9 million initial claims filed the week ending April 25 and filings have fallen for five weeks in a row.

The claims numbers come one day before the release of the April jobs report, which is expected to show a staggering jump in unemployment to around 16%.

The Congressional Budget Office has projected that unemployment, which hit 4.4% in March, will average nearly 14% during April, May and June. Moody's Investors Service predicts it will rise to 15% during the quarter.

The real unemployment rate is probably higher, says Elise Gould, a senior economist at the Economic Policy Institute.

"I think we are not near the peak yet," she says. "I think we are still going to see additional job losses show up in the data for May, for June. Unfortunately, I don't think this has gotten as bad as it will get yet."

One sign of how much damage the job market has sustained came Wednesday, when the ADP Research Institute said the private sector alone lost more than 20.2 million jobs last month, a record. The previous record was 835,000 jobs cut in February 2009, during the height of the Great Recession.

The crisis has hit all kinds of businesses, from neighborhood restaurants to well-known names like Airbnb, which is cutting a quarter of its workforce; Boeing, which is slashing about 16,000 jobs; and the J.Crew clothing chain, which filed for bankruptcy this week.

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