The population of a southern city follows the exponential law. If the population doubled in size over 2929 months and the current population is 30 comma 00030,000, what will the population be 33 years from now
Hard to say what your numbers are, but if it doubles every 29 months, and it is now 30,000, then in 33 years it will be
30000*2^(33*12/29)
If I got the numbers wrong, then fix them and the evaluate.
P*2^(t/n)
start at P
double in n years
t is years from start.
To find the population 33 years from now, we need to use the exponential formula for population growth, which is given as:
P(t) = P₀ * e^(rt)
Where:
P(t) = the future population at time t
P₀ = the initial population
e = Euler's number (approximately 2.71828)
r = the growth rate
t = time
First, let's find the growth rate, which is the constant "r" in the formula. We know that the population doubled in size over 2929 months, which is equivalent to 243.42 years.
The formula for finding the growth rate is:
r = ln(2) / t
Where:
ln = natural logarithm
2 = doubling of population
t = time period in years
r = ln(2) / 243.42
Now, let's calculate the growth rate:
r ≈ 0.002852
Next, we can use the given current population P₀ = 30,000 to find the future population P(t) 33 years from now. We convert 33 years to months, which is 396 months.
P(t) = 30,000 * e^(0.002852 * 396)
Finally, we calculate the future population:
P(t) ≈ 45,806.08
Therefore, the population 33 years from now is estimated to be approximately 45,806.08.