Question

3. You have a bad cough and have to attend your little sister's choir concert. You take cough drops that contain 100 mg of menthol in each drop. Every minute, the amount of menthol in your body is cut in half. Write a funetion that models the amount of menthol in your body over time. Use x for minutes and y for the amount of menthol, in mg, remaining in your body It is safe to take a new cough drop after the level of menthol in your body is less than 5 mg, How long will it be before you can take another cough drop?

Answer 1

We have the next information

100 mg of menthol

every minute the amount of menthol in your body is cut in half

we have the next variables

x= minutes

y= amount of menthol in mg remaining in your body

so the equation that can we model is

`y=100(0.5)^x`

then we have that It is safe to take a new cough drop after the level of menthol in your body is less than 5 mg

y= 5mg

`5=100(0.5)^x`

in order to know the time we need to solve the equation above

`\begin{gathered} (0.5)^x=(5)/(100) \\ (0.5)^x=0.05 \end{gathered}`

then we isolate the x

`x=4.32`

after 5 minutes you can take another cough drop