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12345Real exponents

Solutions to the exercises

Exercise 1
a

A ( 10 ) = 25000 1.1 10 64844

b

A ( 10 7 12 ) 68551

c

1.1

d

1.1 1 12 1.008 so approximately 0.8 % per month.

e

A ( -5 ) 15523 en A ( -10 ) 9639

f

Check that A ( -5 ) 1.1 -5 = A ( -10 ) .

Exercise 2
a

1-1-2001: € 7518.15
1-1-2000: € 7092.60
1-1-1999: € 6691.13

b

On january 1, 1996.

c

He deposited € 5000 on 1 January 1994.

Exercise 3
a

g 3 uur = 3000 1200 = 2.5

b

g ( 1 hour ) = ( 2 . 5 ) ( 1 3 ) 1 . 357 so 35.7% per hour.

c

H ( t ) = 1200 1.357 t

d

Around two and a quarter hours before t = 0 .

Exercise 4
a

0 - 1500: approximate yearly growth rate 1.00046 , so approximate growth percentage 0.05 % per year
1500 - 1800: approximate yearly growth rate 1.002313 , so approximate growth percentage 0.23 % per year
1800 - 1950: approximate yearly growth rate 1.00463 , so approximate growth percentage 0.46 % per year
1950 - 1986: approximate yearly growth rate 1.01944 , so approximate growth percentage 1.94 % per year

b

1500 - 1750: approximate yearly growth rate 1.00115 , so approximate growth percentage 0.12 % per jaar
1750 - 1800: approximate yearly growth rate 1.00814 , so approximate growth percentage 0.81 % per year
1986 - 1997: approximate yearly growth rate 1.01735 , so approximate growth percentage 1.74 % per year

Exercise 5

The permitted content is called A , after the accident the actual content is 6 A . Then ( 1 2 ) t 6 A = A and this gives ( 1 2 ) t = 1 6 . Using the GRC you find t 2 . 58 , so 2.58 periods of 8 days. That is 20.68 days. The hay should be stored 21 days.

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