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

Answer:

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

Step-by-step explanation:

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

Lets take the terms as $c=\frac{k}{t}$,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...$k=c\times( t)$

$t=30\ sec=\frac{30}{60} =0.5\ min$ and $c=4$

$k=0.5\times 4=2$

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

So for this we have been given,$t=120\ sec=\frac{120}{60} = 2\ min$ and $k=2$.

As $c=\frac{k}{t} =\frac{2}{2} =1$

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

Answer 2

Answer:

c=120/t  Loris expected cavities: 1 cavity

Step-by-step 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.