SMARTPHONE A new smartphone application is available for download. The number \( y \) of downloads can be modeled by the function \( y=6.3 x^{2}+3000 \), where \( x \) is the number of hours since the new application was released. How many hours does it take for the number of downloads to reach 3630 ? (Section 8.3)

To find how many hours it takes for the downloads to reach 3630, we can set the function equal to 3630: \[ 6.3x^2 + 3000 = 3630. \] Subtract 3000 from both sides: \[ 6.3x^2 = 630. \] Now, divide both sides by 6.3: \[ x^2 = 100. \] Taking the square root of both sides gives us: \[ x = 10. \] So, it takes 10 hours for the number of downloads to reach 3630. Reaching 10 hours may seem like just a number, but think about the excitement of new app downloads! The buzz usually peaks shortly after release as people rush to check it out, leading to awesome spikes in download numbers that app developers love to celebrate! When working with quadratic functions like this, it can be easy to overlook signs or forget to simplify step-by-step. Always double-check your calculations and ensure you handle each term correctly—even small mistakes can lead you down the wrong path. Happy calculating!