Exponential relations > Exponential growth
1234Exponential growth

Solutions to the exercises

Exercise 1
a

1.5

b

1 . 5 2 = 2 . 25 , so the surface area increases with 125% in two days.

c

yes, with growth rate 1.5 until the entire surface is covered.

Exercise 2
a

After 1 year € 4440 and after 2 years € 4928,40.

b

1.11

c

Multiply by 1.11 .

d

Divide by 1.11 .

e

( 7279 . 45 ) ( 6740 . 23 ) 1 . 08 , so the growth rate is 1.08 and the percentage of growth is 8%.

Exercise 3
a

N ( t ) = 5000 0 . 96 t

b

N ( 10 ) 3324

c

N ( 17 ) 2498 , so after 17 years.

Exercise 4
a

Calculate the ratios of each two concecutive numbers. You find approximately 1.042 .

b

4.2% per year.

c
d

After 10 years.

e

K ( 5 ) 19254 . 15 and K ( 10 ) 23425 . 61

f

It makes no difference.

Exercise 5
a

School 1 with a growth rate of 0.95 , so 5% decay.

b

Linearly, 45 students less per year.

c

No, school 2 will have 0 students in the end and in school 1 the number of students decreases slower and slower.

d

The number of students only changes incidentally during a year. There is a structural change of the number at the beginning of the school year only, depending on the applications and the exam results.

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