It is predicted that garden gnome value will go up by 2% each year, forming a geometric progression. Jean-Claude has a garden gn
ome 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.
1 answer:
Answer:
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 .
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