Respuesta :
It will take approximately 19 hours to dissolve before there is only one gram left.
Exponential decay function:
The exponential decay function is used to find the rapid decrease over a period of time i.e. the exponential decrease.
The quantity decreases slowly after which the rate of change decreases over a period of time rapidly. This decrease is calculated by using the exponential decay formula.
The exponential decay formula is
[tex]P(t) = P_{0}e^{-rt}[/tex]
where:
P(t) = the amount of some quantity at time t
Pā = initial amount at time t = 0
r = the decay rate
t = time (number of periods)
Given:
A patient ingests 20 grams of a certain drug which dissolves away at a constant rate of 15% per hour.
To find the time take to dissolve before there is only one gram left.
Initial amount of substance = Pā = 20 grams
Decay rate = r = 15%
=> 15/100 = 0.15
Remaining quantity = P(t) = 1
So, apply the values on the formula
[tex]1=20\times e^{-0.15\times t}[/tex]
When we simplify it,
we get the value of t as ā 19.971
To know more about Exponential decay here
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