Based on the information available, the price prediction for API3 (API3) varies across different sources for the next week. Here's a summary of the predictions:

1. CoinCodex predicts the price of API3 to increase by 37.17%, reaching $4.22 by June 10, 2024.

2. Another source suggests a 5% increase in the next 30 days, potentially reaching $2.620981.

3. A third source indicates a more conservative estimate with a 12.62% increase in the next week, which would put the price around $3.066 - $3.49.

4. A fourth source predicts a 3.66% decrease in the next 24 hours, which may not directly provide a next week prediction but suggests a short-term bearish trend.

5. A fifth source mentions a 10.11% price increase in the last 24 hours, but does not provide a specific price prediction for the next week.

Please note that these predictions are based on different methodologies and should be taken with a grain of salt. Cryptocurrency markets are volatile and subject to rapid changes. Always do your own research and consider multiple sources before making investment decisions.