Answer:
1.5% will remain at 6.00pm.
Step-by-step explanation:
The function for exponential decay is,
[tex]y(t)=Ae^{rt}[/tex]
where,
y(t) = the future amount,
A = initial amount,
r = rate of growth,
t = time.
A researcher measures 200 counts per minute coming from a radioactive source at noon.
At 3:00pm, i.e after 3 hours,she finds that this has dropped to 25 counts per minute.
Putting the values,
[tex]\Rightarrow 25=200e^{r\times 3}[/tex]
[tex]\Rightarrow \ln \dfrac{25}{200}=\ln e^{r\times 3}[/tex]
[tex]\Rightarrow \ln \dfrac{1}{8}={r\times 3}\times \ln e[/tex]
[tex]\Rightarrow \ln \dfrac{1}{8}={r\times 3}\times 1[/tex]
[tex]\Rightarrow \ln \dfrac{1}{8}={r\times 3}[/tex]
[tex]\Rightarrow r=\dfrac{\ln \dfrac{1}{8}}{3}=-0.6931[/tex]
-ve sign means the amount is decreasing.
As we have to find the amount at 6.00pm i.e after 6 hours, so
[tex]y(t)=200e^{-0.6931\times 6}=3.13\approx 3[/tex]
As number of bacteria can't be in decimal.
So the percentage will be,
[tex]=\dfrac{3}{200}=0.015=1.5\%[/tex]
