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

Explanation:

Given

Initial amount of bacteria
`x_o=20`

Final Population of bacteria
`x=2000`

`r=0.825`

Using formula

`x=x_o(2)^{(T)/(r)}`

where T=time in days

`2000=20(2)^{(T)/(0.825)}`

`100=2^{(T)/(0.825)}`

Taking log both side

`\log_(10) (100)=\log _(10) (2^{(T)/(0.825)})`

`2=(T)/(0.825)\log _(10)2`

`T=(2* 0.825)/(\log 2)`

`T=5.48\ days`