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The initial population of a town is 3700, and it grows with a doubling time of 6 years. Determine how long it will take for the population to quadruple.

Answer :

Final Answer:

It will take approximately 18 years for the population to quadruple, considering the initial population of 3700 and a doubling time of 6 years.

Explanation:

Given that the population of the town grows with a doubling time of 6 years, we can use the concept of exponential growth to solve this problem. The doubling time indicates the time it takes for the population to double in size.

Let's denote [tex]\( P_0 \)[/tex] as the initial population (3700) and [tex]\( t \)[/tex] as the time in years. The exponential growth formula can be expressed as:

[tex]\[ P(t) = P_0 \times 2^{(t/T)} \][/tex]

Where [tex]\( T \)[/tex] is the doubling time. In this case,[tex]\( T = 6 \)[/tex] years. Now, we want to find out how long it will take for the population to quadruple, which means the final population [tex]\( P(t) \)[/tex] should be four times the initial population [tex]\( P_0 \)[/tex]:

[tex]\[ P(t) = 4 \times P_0 \][/tex]

Substitute the values:

[tex]\[ 4 \times 3700 = 3700 \times 2^{(t/6)} \][/tex]

Solving for [tex]\( t \)[/tex], we have:

[tex]\[ 4 = 2^{(t/6)} \][/tex]

[tex]\[ \log_2 4 = \frac{t}{6} \][/tex]

[tex]\[ 2 = \frac{t}{6} \][/tex]

[tex]\[ t = 12 \][/tex]

So, it will take approximately 12 years for the population to quadruple.

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