Answer :
Every second, the number of harmful bacteria remaining in the body decays by a factor of approximately .
To determine the rate of change in the number of harmful bacteria remaining in the body every second, we need to convert the time in the given function from minutes to seconds. The function provided is
⇒ [tex]H_{minute}[/tex](t) = 500,000,000 · [tex](0.2)^t[/tex].
A minute has 60 seconds, so we need to express the decay factor for a second. By letting t = [tex]t_{seconds}[/tex] ÷ 60, we can rewrite the function in terms of seconds:
⇒ [tex]H_{second}[/tex](t) = 500,000,000 · [tex](0.2)^\frac{t}{60}[/tex].
For every passing second, the decay factor is [tex](0.2)^\frac{1}{60}[/tex]. Using a calculator, we find:
⇒ [tex](0.2)^\frac{1}{60}[/tex] ≈ 0.98855,
rounded to two decimal places.
Therefore, every second, the number of harmful bacteria remaining in the body decays by a factor of approximately 0.99.
Complete question:
After a certain medicine is ingested, the number of harmful bacteria remaining in the body declines rapidly.
The relationship between the elapsed time t, in minutes, since the medicine is ingested, and the number of harmful bacteria remaining in the body, [tex]H_{minute}[/tex](t), is modeled by the following function:
[tex]H_{minute}[/tex](t) = 500,000,000 · [tex](0.2)^t[/tex]
Complete the following sentence about the rate of change in the number of harmful bacteria remaining in the body in seconds.
Round your answer to two decimal places.
Every second, the number of harmful bacteria remaining in the body decays by a factor of .
