The population of a southern city follows the exponential law. If the population doubled in size over 13 months and the current population is 30,000 what will the population be in 5 years from now?
The population of a southern city follows the exponential law. If the population doubled in size over 10 months and the current population is 40,000 what will the population be 5 years from now?
in chronological order list the events that led up to the embargo act and describe each event
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To find the population in 5 years, we need to first determine the growth rate of the city's population using the given information.
The exponential growth equation can be represented as:
P = P0 * e^(rt)
Where:
P = population after time t
P0 = initial population
e = Euler's number (approximately 2.71828)
r = growth rate (in decimal format) - represents the rate at which the population increases over time
t = time (in this case, 5 years)
We are given that the population doubled in size over 13 months, which is approximately equal to 1.083 years.
Let's calculate the growth rate (r) using this information:
P0 = 30,000 (current population)
P = 2 * P0 (doubled population)
t = 1.083 years
Using the exponential growth equation, we can solve for the growth rate (r):
2 * P0 = P0 * e^(r * 1.083)
2 = e^(1.083 * r)
Taking the natural logarithm of both sides to isolate the exponential term:
ln(2) = 1.083 * r * ln(e)
Since ln(e) is equal to 1, we can simplify further:
ln(2) = 1.083 * r
Now we can solve for the growth rate (r):
r = ln(2) / 1.083
Once we have the growth rate (r), we can substitute it back into the exponential growth equation to calculate the population after 5 years:
P = P0 * e^(r * t)
t = 5 years
P = 30,000 * e^(r * 5)
Calculating the value of e^(r * 5), where r is the previously calculated growth rate, will give us the population in 5 years.
let the equation be
population = current (2)^(t/13) , where t is in months
in 5 years, t = 60
population = 30000(2)^(60/13) = appr 735,000
(a rather silly question)
check for reasonableness of answer:
after 13 months -- 60000
after 26 months --120,000
after 39 months -- 240,000
after 52 months -- 480,000
after 65 months -- 960,000
our answer is reasonable according to the data given, but certainly not realistic.