Question

Warm Up 1/13/21A biologist is studying a variety of bacteria. She has calculated that a colony of this bacteria - given enough food andspace - will double its population every hour.Answer the following questions:If she starts a colony of the bacteria with a population of 1,000:a) How many bacteria will be in the colony after 6 hours?b) If the colony has grown to a population of 1,234,567, approximately how long was it allowed to grow from theinitial population?

Answer 1

A)

starts off with 1000 and doubles every hour, so in 6 hours we will have 6 "doublings", Thus:

1000 * 2 * 2 * 2 * 2 * 2 * 2 = 64,000 bacteria

B)

the final population is 1,234,567. We can say:

`1,234,567=1000\cdot2^x`

Now, we solve for x:

`\begin{gathered} 1234.567=2^x \\ \ln (1234.567)=\ln (2^x) \\ \ln (1234.567)=x\ln (2) \\ x=(\ln (1234.567))/(\ln (2)) \\ x=10.27 \end{gathered}`

t = 10.27 hours