An extensive and expensive search party
As they flew over Gardner Island, they noted that there were signs of human dwelling but there were no signs of anyone looking for help. They circled and zoomed over the island several times and nobody showed up looking for help.
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The US government did not give up. They did an extensive search effort that cost millions of dollars. But after several months of having no clues, they had no choice but to call off the search. Earhart was declared dead in absentia by January 5, 1939.
She was an icon
Earhart was already a cultural icon before she disappeared. Even if she vanished into thin air, the world never forgot her name. Several memorials and countless tributes were organized in her honor.
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The unsolved mystery of her disappearance just added to her fame. She was now a feminist icon that inspired a lot of girls to take up flying. Her life has been immortalized in movies and books.