Question

if the national economy shrank at an annual rate of 6% per year for 3 consecutive years, then the economy shrank by 18% over the three year period. The economy shrank by what per6 over the three year period?

Answer 1

You want to find x such that

... 1 - x = (1 - 6%)³

... x = 1 - (0.94)³ = 1 - 0.830584 = 0.169416

... x ≈ 16.9%

The economy shrank by about 16.9% over the three-year period.

Answer 2

Using an exponential function, it is found that the economy shrank by 16.94% over the three year period.

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The equation for a decaying exponential amount is given by:

$A(t) = A(0)(1 - r)^t$

In which:

• A(0) is the initial value.
• r is the decay rate, as a decimal.

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• Shrank 6% per year, thus $r = 0.06$, and:

$A(t) = A(0)(1 - r)^t$

$A(t) = A(0)(1 - 0.06)^t$

$A(t) = A(0)(0.94)^t$

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• After 3 years:

$A(3) = A(0)(0.94)^3$

$A(3) = 0.8306A(0)$

$1 - 0.8306 = 0.1694$

0.1694*100% = 16.94%.

The economy shrank by 16.94% over the three year period.

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