Answer:
11.72 hours
Explanation:
In a continuous exponential growth model, the formula for the size of the population at time t is given by:
N(t) = N₀ * e^(rt)
where N₀ is the initial population size, r is the growth rate parameter, and e is the mathematical constant approximately equal to 2.71828.
To find the time it takes for the population size to double, we can set N(t) equal to 2N₀ and solve for t:
2N₀ = N₀ * e^(rt)
Dividing both sides by N₀:
2 = e^(rt)
Taking the natural logarithm of both sides:
ln(2) = rt * ln(e)
Since ln(e) = 1:
ln(2) = rt
Solving for t:
t = ln(2)/r
Substituting the given growth rate parameter of 5.9% per hour:
t = ln(2)/(0.059) ≈ 11.72 hours
Therefore, it takes approximately 11.72 hours for the size of the population to double.