Problem

$m^{2}[2]$ (e) The value of the campsite has increased exponentially by $1.5 \%$ every year since it opened 30 years ago. Calculate the value of the campsite now as a percentage of its value 30 years ago.

Solution

Step 1 :Let the initial value of the campsite be \(V_{initial} = 1\)

Step 2 :The growth rate is \(1.5\% = 0.015\)

Step 3 :The number of years is \(30\)

Step 4 :Calculate the value now using the formula: \(V_{now} = V_{initial} * (1 + growth\_rate)^{years}\)

Step 5 :\(V_{now} = 1 * (1 + 0.015)^{30} = 1.5630802204908514\)

Step 6 :Calculate the percentage: \(Percentage = \frac{V_{now}}{V_{initial}} * 100\)

Step 7 :\(Percentage = \frac{1.5630802204908514}{1} * 100 = 156.30802204908514\)

Step 8 :\(\boxed{156.31\%}\) is the value of the campsite now as a percentage of its value 30 years ago

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Source: https://solvelyapp.com/problems/11754/

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