Question

paul a dentist determined that the number of cavities that develops in his patients mouth each year varies inversely to the number of seconds spent brushing each night.

Answer 1

c=120/t Loris expected cavities: 1 cavity

Explanation:

We are given that c, the number of cavities Lori will have, varies inversely with amount of time, t, she spent brushing, so c=k/t for some constant, k. To determine the value of k, substitute the known values, c=4 when t=30, to find that

4=k/30

Multiplying by 30 gives k=120, so an equation that relates c and t is

c=120/t

Substituting t=120 gives

120/120=1

So Paul would expect Lori to have 1 cavity if she had brushed her teeth for 120 seconds each night.

Answer 2

Lori will have
`1` cavity if she brushed for
`120\ sec` each night.

Explanation:

As the question suggests cavities developed varies inversely with the number of seconds spent on brushing.

Lets take the terms as
`c=(k)/(t)`,where
`k` is the constant of proportionality.

And

c = Number of cavities developed each year

t = Number of minutes spent on brushing per night

Now we will plugging the values of the given terms and find the value of
`k`,for this we can re-arrange it as...
`k=c*( t)`

`t=30\ sec=(30)/(60) =0.5\ min` and
`c=4`

`k=0.5* 4=2`

Now as Lori will increase her brushing time so as the cavity will decrease.

So for this we have been given,
`t=120\ sec=(120)/(60) = 2\ min` and
`k=2`.

As
`c=(k)/(t) =(2)/(2) =1`

So as per Paul's observation if Lori brushed for
`2\ mins` at night she will have
`1` cavity on that year.