Question

A bacterial colony doubles in size every 30 minutes. If initially there are 40 bacteria present, the number of bacteria after t minutes can be modeled by the function N(t) = 40 - 2t/30How long does it take until there are 1,000 bacteria?

Answer 1

`N(t)=40\cdot2^{(t)/(30)}`

N=1000

we need to clear t of the model

`1000=40\cdot2^{(t)/(30)}`
`(1000)/(40)=2^{(t)/(30)}`
`25=2^{(t)/(30)}`
`(t)/(30)=\log _225`

`(t)/(30)=(\log 25)/(\log 2)`
`t=(\log 25)/(\log 2)(30)=139.31`