It is predicted that garden gnome value will go up by 2% each year, forming a geometric progression. Jean-Claude has a garden gnome currently valued at £80,000. If the rate of inflation is correct: a) What will Jean-Claude's gnome be worth after 1 year?

b) What is the common ratio of the geometric progression?

c) What will Jean-Claude's gnome be worth after 10 years?

d) It will take k years for the value of Jean-Claude's gnome to exceed £120,000. Find k.

Step-by-step explanation:

a ) The worth of Jean-Claude's gnome after 1 year

= 80000 x 1.02

=  £81600

b ) common ratio of geometric progression

= 81600 / 80000

= 1.02

c )  worth after 10 years

= 80000 x 1.02¹⁰

= 80000 x 1.21899

= £97519.55

d )

120000 = 80000 x

1.5 =

ln1.5 = k ln 1.02

k = ln 1.5 / ln 1.02

= .4054 / .0198

= 20.47 years .

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you