Question

The virus of a culture decreases at the rate of 5% due to a medicine.the virus count was 2×10^7 at 10AM.find the virus count at 1pm.

Answer 1

Please tell the time at which the 5% decrease that is 1hour or 1 min or 1 sec

Answer 2

Answer:

The virus count at 1:00 PM is $1.97\times 10^7$

Step-by-step explanation:

Assuming that the virus is decreasing at the rate of 5% per hour

If the initial number of virus are N and the rate of decreasing is r then after n hours, the virus remaining will be

$N'=N(1-\frac{r}{100})^n$

From 10 AM to 1 PM total number of hours passed = 3

Given $N=2.3\times 10^7$

$r=5\%$

Thus,

$N'=N(1-\frac{r}{100})^n$

$N'=2.3\times 10^7(1-\frac{5}{100})^3$

$\implies N'=2.3\times 10^7(1-\frac{1}{20})^3$

$\implies N'=2.3\times 10^7(\frac{19}{20})^3$

$\implies N'=2.3\times 10^7\times \frac{6859}{8000}$

$\implies N'=1.97\times 10^7$

Hope this helps.