The biggest hole is that the doubling time is usually closer to 7 days (10% growth in cases per day) than to 3 days (41% growth in cases per day). We do see 41% daily growth in reported cases in times where the testing is catching up to a much larger population of undetected cases, but overall 7 days is a more reasonable doubling time. On that assumption, 2040 × 2⁴·⁴ = 43068 actual cases in the Bay Area in a month.
When you're modeling exponential growth, most of your possible errors are just an additive time shift, a small one if the growth is rapid. For example, if the actual current cases are 4080, a 100% error in the estimate above of 2040, that just moves the time to reach those 43068 cases from 31 days away to 24 days away. But an error in the exponential growth rate is a multiplicative time distortion, leading to an exponentially large error at any given point in the future.
When you're modeling exponential growth, most of your possible errors are just an additive time shift, a small one if the growth is rapid. For example, if the actual current cases are 4080, a 100% error in the estimate above of 2040, that just moves the time to reach those 43068 cases from 31 days away to 24 days away. But an error in the exponential growth rate is a multiplicative time distortion, leading to an exponentially large error at any given point in the future.