Problem Solutions

<#54#>Section 7.3<#54#>

• <#111#><#56#>#12:<#56#><#111#>

  #displaymath116#

• <#112#><#67#>#49:<#67#><#112#> (Bacteria population problem)

  The population of bacteria as a function of time (in hours) is given by

  #displaymath117#

  a) Find the inverse and explain its meaning.

  Take logs of both sides (and you can use either ln, or #tex2html_wrap_inline126#). Let's use ln:

  #displaymath118#

  Solving for t, we have

  #displaymath119#

  This represents the amount of time in hours to reach population n.

  b) Now we solve for n=50000:

  #displaymath120#

  or about 27 hours.