Flashcard 9 - Mathematics: Algebraic Reasoning Flashcard Set for the TSIA2

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The correct answer is:

It represents the growth factor of the population with a \(30\%\) growth rate per year.


Explanation:

The exponential growth model is given by the equation:

\[a = a_{0}(1+r)^t\]

Where \(a\) is the final amount, \(a_{0}\) is the initial amount, \(r\) is the growth rate, and \(t\) is the time period.

Looking at our equation \(P = 1000(1.3)^5\), we can clearly see that \(1.3\) is the growth factor. Solving for \(r\):

\[1.3 = 1 + r\] \[r = 1.3 - 1\] \[r = 0.3\]

In percent, that is \(0.3 \times 100 = 30\%\). So, \(1.3\) represents the growth factor with a growth rate of \(30\%\).

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