Exponential functions > Exponential growth
12345Exponential growth

Solutions to the exercises

Exercise 1
a

R ( t ) = 2 3 t

b

See table.

t 0 1 2 3 4 5
R(t) 2 6 18 54 162 486
c

During the sixth year.

Exercise 2
a

2 7 = 128

b

2 11 = 2028

c

2 3 = 8

d

2 62 4 . 6117 × 10 18

Exercise 3
a

N ( t ) = 5000 0.96 t

b

N ( 10 ) 3324

c

0.96 10 0.6648 , this corresponds to a decrease of approximately 33.52 %.

d

N ( 17 ) 2498 , so after 17 years.

Exercise 4
a

3 3

b

3 1

c

1 = 3 0

d

4 3

Exercise 5
a

Taking the ratio of each two consecutive values each time results in approximately 1.042 .

b

4.2 % per year.

c

See table.

year 0 1 2 3 4 5 6 7 8 9 10
amount 10000.00 10800.00 11664.00 12597.12 13604.89 14693.28 15868.74 17138.24 18509.30 19990.05 21589.25
d

After 10 years.

e

K ( 5 ) 19254.15 and K ( 10 ) 23425.61

f

This does not make a difference.

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