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].