the opposite or addictive increase of 5x is -5x.
the opposite or addictive increase of 5x + 8 is -5x -8.
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]
So,
We can notice that the graph of g, is translated 2 units to the left and 4 units up. We can express these changes with the following equation:
Well, first consider how many digits there are. You have 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0, depending on how you use it, that are all digits.
If you count 0 as a digit other than a place holder (0000, 0001, etc.), you would end up with ten thousand (10,000) numbers with four digits, starting with 0000, and ending with 9999. If you count 0 as nothing other than a place holder (1000, 1001, etc.), you would have nine thousand (9,000) numbers with four digits, starting with 1000.
So, depending on how you view 0, you can make up to 10,000 different numbers that contain four digits.
Read it carefully. It's telling you the answer in the problem! There is one teacher for every 11 students. Of course there are more students!
