Determine whether y = 5(0.6)^t represents exponential growth or exponential decay. Then identify the percent rate of change.

Question

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Answer 1

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Answer 2

It is exponential decay for t > 0.

 

Multiplying an initial quantity by 0.6 leaves 60% of that quantity, which is a reduction of 40%.  For example, if t = years, then at the end of a year, you are left with 40% less than what you had at the start of the year.  If you repeat this for t years, the final amount (assuming you started with 5 at the very beginning) is

 

y(t) = 5 (0.6)^t

Answer 3

The growth rate is less than one.  Therefore, it is decay.  You can rewrite it as

 

y = 5(1 - 0.4)^t

 

where the decay rate is 40%.