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, \[b_{\text{second}}(t)\], in the petri dish is modeled by the following function: \[b_{\text{second}}(t)=6000\cdot \left(\dfrac{15}{16}\right)\^{\large t}\] complete the following sentence about the rate of change in the number of bacteria in minutes. round your answer to two decimal places. every minute, the number of bacteria decays by a factor of .

Answer 1

The decay factor for every minute in the given function is 0.95.

Step-by-step explanation:

In the given function, the exponential decay of bacteria is modeled by the equation bsecond(t) = 6000 * (15/16)t, where t is the elapsed time in seconds and bsecond(t) represents the number of bacteria remaining in the dish. To find the decay factor of bacteria in minutes, we need to convert the time to minutes. Since there are 60 seconds in a minute, the decay factor for every minute can be calculated by raising 15/16 to the power of 60. Plugging in the values, we get:

bminute(t) = 6000 * (15/16)60t

Rounding the decay factor to two decimal places, we have every minute the number of bacteria decays by a factor of 0.95.