Question

For a certain strain of bacteria, r, is 0.825 (compounded continuously) when t is measured in days. How long will
it take 20 bacteria to increase to 2000? Round to the nearest hundredth.​

Answer 1

Answer:5.48 days

Step-by-step explanation:

Given

Initial amount of bacteria $x_o=20$

Final Population of bacteria $x=2000$

$r=0.825$

Using formula

$x=x_o(2)^{\frac{T}{r}}$

where T=time in days

$2000=20(2)^{\frac{T}{0.825}}$

$100=2^{\frac{T}{0.825}}$

Taking log both side

$\log_{10} (100)=\log _{10} (2^{\frac{T}{0.825}})$

$2=\frac{T}{0.825}\log _{10}2$

$T=\dfrac{2\times 0.825}{\log 2}$

$T=5.48\ days$