The trendline equation of the data has been found to be \( f(x)=1.35 \cdot(2.71)^{.37 x} \). How many microbes should she expect on day 20 . Round to the nearest whole number.

To find the expected number of microbes on day 20, plug \( x = 20 \) into the equation: \[ f(20) = 1.35 \cdot (2.71)^{0.37 \cdot 20} \] Calculating \( 0.37 \cdot 20 \) gives you \( 7.4 \). Then compute \( (2.71)^{7.4} \): \[ f(20) = 1.35 \cdot (2.71)^{7.4} \approx 1.35 \cdot 610.587 \approx 825.79 \] Rounding to the nearest whole number, she should expect approximately 826 microbes on day 20. Isn’t it fascinating how we can model the growth of microbes with math? Science gives us the power to predict outcomes based on observed trends—something that impacts not just laboratory studies, but also agriculture, health, and even environmental science! To double-check your calculations, verify at each step: ensure you're applying the exponent correctly and using a reliable method for multiplication. Mistakes often creep in during calculator use, particularly with exponential growth. A small error could lead to an incredible difference in results!