Question one. TV shows. Like at least one. This mean th

Question one
A. TV shows
I. Like at least one
This mean the number of students who like one TV shows and above
The solution is 43+ 44+ 24 ¿=111
II. At most one
This means the number which like a total of one show at most
Game of thrones only 26
Prison Break only 24
24 only 9
No TV show liked 39
Hence at most one (one or zero shows) gives 98 students
III. Game of thrones or 24 only
Game of thrones only 26
24 only 9
Total 35
IV. Prison break and 24
8 students
V. Game of thrones only 26 students.
B. Taking apple juice only 25
Taking orange juice only 75
Taking both apple and orange 75
Total 175
Taking neither of the juices 225 students
Question two
A. Population follows; p ( t ) =20 ert
P is the population in thousands, t the number of years since 1980 and r the growth rate
which is 10%.
I. As at 1999
1999−1980=19

p ( 19 )=20 e(0.1∗19)=133.7179
Hence P is 133,718
II. In 2020
t=2020−1980=40
p ( 40 ) =20 e(0.1∗40)=1091.9630
P is 1,091,963
III. The population was 105000 in which year
p ( t ) =20 ert =105000
20 ert= 105000
1000 =105
20 ert=105
ert=5.25
e0.1 t =5.25
0.1 t=ln 5.25
t=16.58
The year is ( 1980+16.58 ) =1996.58
Which is 1996
IV. p ( 35 )=20 e35 r=182000
20 e35r =182
e35 r=9.1
35 r=ln ( 9.1)
r = ln ( 9.1 )
35 =0.06309=6.31 %
B. Solve for x
log5 ( x−10 ) −log5 3=2
That means
log5 ( x−10
3 )=2
52= ( x−10
3 )

25=( x−10
3 )
75=x−10
x=85
C. 7 e3 x−5 +7.9=47
7 e3 x−5=39.1
e3 x−5= 39.1
7
3 x−5=ln ( 39.1
7 )
x=2.2401
Question three
A. Investment
δ=ln (1+i)
Barclays
δ=ln ( 1.132 ) =0.12399
Standard Chartered
δ=ln ( 1. 0 3 5 )=0.0344
I. At time t
Amount in Barclays is
A=7500 e0.12399 t
Amount∈ Standard Chartered is
A=11000 e0.0344 t
Equating the same
7500 e0.12399t =11000 e0.0344 5 t
e0.12399t = 11000e0.0344 t
7500
e0.12399t
e0.0344t = 11000
7500