If the national economy shrank at an annual rate of 7% per year for three consecutive​ years, then the economy shrank by 21% over the three-year period.

Question

I need to find out how much the economy actually shrank by

Answer 1

if E = economy

 

E = E₀(1-r)^t

E = final or future national economy

E₀ is the starting value of E

r = shrinkage rate as a decimal=.007

t is the time

 

 

E = E₀ (1-.007)³

E = E₀(.93)³

 

As Kenneth said:

.93³ = .8044

 

E = .8044E₀

 

The final national economy is 

80.44% of the beginning value

showing a shrinkage of 19.56%

Answer 2

no, the resulting economy measure would be original measure multiplied by 0.93³ = 0.8044 so that would be 19.56% shrinkage.