Studies have shown that the number of bacteria on a public restroom sink can grow exponentially from 5,000 bacteria to 12,000 bacteria in 10 hours. Write the natural logarithmic equation that would represent how the number of bacteria would grow over the given time period. Use the exponential growth/decay formula, , where represents the number of bacteria after hours, is the initial number of bacteria, and is the rate of growth or decay. Given the rate of bacterial growth, how many bacteria would there be after 24 hours? How many bacteria would you expect to be present after 48 hours? Verify your answers algebraically.

Determine the growth rate, , using properties of logarithms.

Determine the number of bacteria after 24 hours.

Determine the number of bacteria after 48 hours.

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