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The number of fish in a lake declined by 30% over 13 years. What is the average yearly decline in the number of fish?

I know how to increase, but I can't seem to figure out how to calculate decline, can anyone help explain?

Tyberius
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user424580
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  • There is usually nothing more than a negative sign that differentiates a decrease from an increase. Give it another try and you may get it! – frederick99 Mar 11 '17 at 15:53
  • if it was increase by 30% in 13 years it would be: 1+30/100 = 1.3 13√1.3 = 1.02 -1 0.02 x 100 = 2.0%

    So instead i try with a negative sign: 1-30/100 = 0.7 13√0.7 = 0.97 + 1 1.97 x 100? = defiantly wrong answer.. :S

     – user424580 Mar 11 '17 at 16:05

2 Answers2

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Hint...Decreasing by $30$% is equivalent to multiplying the initial total by $0.7$

So you need to find $x$ such that $$(1-\frac{x}{100})^{13}=0.7$$

David Quinn
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If you really think,$$V=U(1+r)^n$$ where $V$ is final quantity, $U$ is initial quantity (i.e., $1$ in this case), $r$ is the annual rate of change (increase or decrease) and $n$ is the no. of years in this case.

Putting $V=1-0.3=0.7$ and $n=13$, you get $r=-0.02706357116766167$.

That is, a decrease of $2.7\%$ every year.

frederick99
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