Question

An adult takes 600 milligrams (mg) of ibuprofen. Each hour, the amount of ibuprofen in the person's system decreases by one-third. Write the function that models the exponential change between the number of hours, t, and the number of milligrams of ibuprofen remaining in the person's system, m(t). m of t equals 600 times one third to the t power m of t equals negative 600 times one third to the t power m(t) = 600 · 3t m(t) = –600 · 3t

Answer 1

`M_((t))` = 600
`(1)/(3)^t`

Explanation:

y = q
`(b)^t`

:

Where ‘ q ‘ = [ initial value ]

Where ‘ b ‘ = [ decreasing factor ( fraction type ) ]

‘ y ‘ = amount left over

`M_((t)) = 600 (1)/(3) ^ t`

Is your answer..

Answer 2

m(t) = -600 × (1/3)^t

Explanation:

Amounts are in mg.

Start: 600

Since the amount decreases by 1/3 each hour. The amount of change as a function of time in hours is:

After 1 hour: -600 × 1/3

After 2 hours: (-600 × 1/3) × 1/3 = -600 × 1/9 = -600 × (1/3)²

After 3 hours: (-600 × 1/3 × 1/3) × 2/3 = -600 × 1/27 = -600 × (1/3)³

After t hours: -600 × (1/3)^t

Answer: m(t) = -600 × (1/3)^t