This shows that
value= 176.8/200=0.883
Do same thing with the other values in the table we will get a table like this
|
Month
|
Weight
|
Average
|
|
0
|
200
|
0.883
|
|
1
|
176.6
|
0.860
|
|
2
|
151.8
|
0.914
|
|
3
|
138.8
|
0.852
|
|
4
|
118.2
|
0.876
|
|
5
|
103.6
|
0.878
|
|
6
|
91
|
---
|
By adding the average value we will get
Average=5.263/6=0.877
Let consider the exponential junction will become like this
y=ah^x
h is considered as an exponential decay rate of the radioactive substance and on the other hand, ‘a’ is considered as the starting amount of the radioactive substance
this shows that
a=200,h=0.877
Putting these values into the equation it will become like this
y=200×(0.877)^x
Part 4
Part 5
In the part 3 it can be noted that y is considered as the weight of the radioactive substance and on the other hand x is considered as number of months required for the decay.
Part 6
Half-life of the radioactive material
for that case, let consider the value of y= 100 now the equation will become like this
100=200×〖0.877〗^x
100/200= 〖0.877〗^x
0.5=〖0.877〗^x
ln(0.5)=x ln0.877
-0.6931471=x (-0.1312482)
x=0.6931471/0.1312482
x=5.3 months that shows almost 5 months
It shows its half-life is about 5 months
Part 7
After 30 months
This shows x= 30 months now let find the weight of the radioactive material
y=200〖 ×(0.877)〗^30
y=3.9 grams
It shows that after 30 months only 3.9 gram radioactive material will be left
Part 8
How many months passed for 40 gram material
y=40 gram x=¬?
Put the values in the formula
40=200×(0.877)^x
40/200=(0.877)^x
0.2=(0.877)^x
Apply natural log at both ends
ln〖(0.2)=x ln(0.877) 〗
x=12.3 months
It is considered as 12 months when 40 gram radioactive material will be left behind.
Option 2
Part a
Part 2
Part 3
Part 4
If the price is 1750 what will be the demand
This shows that the value of x = 1750 for that case the value of y can be found easily through this
y=-42.29 ln〖1750+479.62〗
y=163.82
Part 5
If demand value is 174 what will be the price
It can be found easily through this formula
174=-42.29 ln〖x+479.62〗
lnx=(479.62-174)/(-42.29)
ln〖x= -7.22〗
x=e^(-7.22)
x= 0.000731
