Exponential functions > Exponential functions
12345Exponential functions

Solutions to the exercises

Exercise 1
a

S ( t ) = 10000 1.05 t

b

Solve 10000 1 . 05 t = 15000 that is 1 . 05 t = 1 . 5 . t = 8 gives 1.4774 and t = 9 gives 1.5513 , so 9 years.

c

Solve 1 . 05 t = 2 . t = 14 gives 1.9799 and t = 15 gives 2.0789 . So 15 years.

Exercise 2
a

1 1 . 05 t = 4000 . Using GC Table: if t = 169 , then € 3810.58 and if t = 170 , then € 4001.11. So 170 years ago.

b

Yes, you could choose - 170 t - 160 .

c

No, there is a horizontal asymptote S = 0 .

Exercise 3
a

g ( 4 months ) = 1630 2000 0 . 815 , so g ( year ) = 0 . 815 3 0 . 541 . 1 year before 6-1-1997 the radiation was 2000 0 . 541 ( - 1 ) 3 695 Bq. 2.5 years after 6-1-1997 the radiation was 2000 0 . 541 ( 2 . 5 ) 431 Bq.

b

S = 2000 0.541 t

c

10 years ago the radiation was 2000 0 . 541 ( - 10 ) 931231 Bq. So B = 0 ; 931231 ] .

d

Solve 0.541 t = 0.5 .
13 months gives 0.514 en 14 months gives 0.4883 Bq. so after 13 months and 16 days, from 22-2-2020.

Exercise 4
a

a ( t ) = 2000 1.04 t and b ( t ) = 1500 1.06 t

b

Enter: Y1=2000*1.04^X and Y2=1500*1.06^X. Window: X from 0 to 20 and Y from 0 to 1000.

c

You find x = 15 . 1028 ... years. This is 15 years and 1.2 month after 1-1-2000, so from 1-3-2015.

Exercise 5

Both curves go through ( 0 , 10 ) . For curve f : at x = 1 the function has the value y = 10 and at x = 2 the value 40, so y = 10 2 x . For curve g : at x = - 1 the function has the value y = 30 and at x = - 2 the value 90, so g ( x ) = 10 ( 1 3 ) x .

Exercise 6

Intersecting H = 650 1 . 055 t and h = 650 + 50 t gives t 12 . 81 .
So after 13 years.

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