Exponential relations > Real indices
1234Real indices

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 and 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 1 January 1996.

c

He deposited € 5000 on 1 January 1994.

Exercise 3
a

g ( 3 hours ) = 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

See table

period growth rate per yer growth percentage
0-1500 1.00046 0.05%
1500-1800 1.002313 0.23%
1800-1950 1.00463 0.46%
1950-1986 1.01944 1.94%
b

See table

period growth rate per year growth percentage
1500-1750 1.00115 0.12%
1750-1800 1.00814 0.81%
1986-1997 1.01735 1.74%
Exercise 5

The permitted content is called A , after the accident 6 A .
Then ( 1 2 ) t 6 A = A and this gves ( 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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