We appreciate your visit to After a certain medicine is ingested the number of harmful bacteria remaining in the body declines rapidly The relationship between the elapsed time tex t. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
We start with the information that after one minute (60 seconds) the bacteria reduce by a factor of [tex]$0.2$[/tex]. This means that if [tex]$d$[/tex] is the decay factor per second, then after 60 seconds the combined decay is
[tex]$$
d^{60} = 0.2.
$$[/tex]
To find [tex]$d$[/tex], we take the 60th root of both sides:
[tex]$$
d = (0.2)^{\frac{1}{60}}.
$$[/tex]
Calculating [tex]$(0.2)^{\frac{1}{60}}$[/tex] gives approximately
[tex]$$
d \approx 0.9735326020510389.
$$[/tex]
When rounded to two decimal places, we obtain
[tex]$$
d \approx 0.97.
$$[/tex]
Thus, every second, the number of harmful bacteria in the body decays by a factor of [tex]$0.97$[/tex].
[tex]$$
d^{60} = 0.2.
$$[/tex]
To find [tex]$d$[/tex], we take the 60th root of both sides:
[tex]$$
d = (0.2)^{\frac{1}{60}}.
$$[/tex]
Calculating [tex]$(0.2)^{\frac{1}{60}}$[/tex] gives approximately
[tex]$$
d \approx 0.9735326020510389.
$$[/tex]
When rounded to two decimal places, we obtain
[tex]$$
d \approx 0.97.
$$[/tex]
Thus, every second, the number of harmful bacteria in the body decays by a factor of [tex]$0.97$[/tex].
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