Finding the rate or time in a word problem on continuous exponential... The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of \( 4.8 \% \) per hour. How many hours does it take for the size of the sample to double? Note: This is a continuous exponential growth model. Do not round any intermediate computations, and round your answer to the nearest hundredth.

In a continuous exponential growth model, the time \( t \) it takes for a population to double can be determined using the formula \( t = \frac{\ln(2)}{r} \), where \( r \) is the growth rate expressed as a decimal. Since your growth rate is \( 4.8\% \), as a decimal, it would be \( 0.048 \). Plugging that into the formula gives us: \[ t = \frac{\ln(2)}{0.048} \approx \frac{0.693147}{0.048} \approx 14.44 \text{ hours}. \] So, it takes approximately \( 14.44 \) hours for the bacteria population to double. When dealing with continuous exponential growth, remember to always check if you're using the correct growth rate! A common mistake is to use the percentage directly instead of converting it to a decimal first. That's key for getting the right calculation. Also, practicing with different growth rates can really help solidify the concept and prepare you for varied problems!