Question

A medication with an initial concentration of 1. 5 milligrams per liter is administered to a

Answer 1

Answer: Exponential decay model:

y

=

x

(

1

−

r

)

t

, half life of tablet is about

2

hours and after

t

=

3

hours , remaining drug on patient's system is

42.875

mg.

Step-by-step explanation: Initial drug

x

=

125

mg ; rate of decay

r

=

30

100

=

0.3

gm/hour

Exponential model:

y

=

x

(

1

−

r

)

t

=

125

(

1

−

0.3

)

t

=

125

⋅

0.7

t

Half life:

y

=

125

2

=

62.5

mg

∴

62.5

=

125

⋅

0.7

t

or

0.7

t

=

1

2

. Taking logarithm on both sides we get ,

t

log

(

0.7

)

=

log

(

0.5

)

∴

t

=

log

(

0.5

)

log

(

0.7

)

≈

1.94

(

2

d

p

)

hour

The half life of tablet is about

2

hours.

After

t

=

3

hours , remaining drug on patient's system is

y

=

125

⋅

0.7

t

=

125

⋅

0.7

3

=

42.875

mg [Ans]