Question

After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly. The relationship between the elapsed time [t], in seconds, and the number of bacteria, [b_ textsecond(t)], in the petri dish is modeled by the following function: [b_ textsecond(t)=6000 cdot left( dfrac1516 right) ^ large t ]. Complete the following sentence about the rate of change in the number of bacteria in minutes. Round your answer to two decimal places.

Answer 1

To find the rate of change in the number of bacteria in minutes, we need to convert the time units from seconds to minutes and substitute the converted time into the given function.

Step-by-step explanation:

The given function bsecond(t) = 6000 * (15/16)t models the relationship between the elapsed time in seconds and the number of bacteria in the petri dish. To find the rate of change in the number of bacteria in minutes, we need to convert the time units from seconds to minutes. There are 60 seconds in one minute, so we can divide the time in seconds by 60. Now we can substitute the converted time into the function and calculate the rate of change in the number of bacteria.

Let's say we want to find the rate of change after 5 minutes. We convert 5 minutes to seconds: 5 * 60 = 300 seconds. Plugging this value into the function, we get bsecond(300) = 6000 * (15/16)300. Perform the calculation to get the rate of change in the number of bacteria in minutes.