The population of a southern city follows the exponential law. If the population doubled over 20 months and the current population is 70,000, what will the population be 5 years from now
growing at the same rate, we have
P(t) = 70000* 2^(t/20)
So, you want P(5*12) = P(60) = 70000*2^3 = 560000
To find the population 5 years from now, we need to use the exponential growth formula:
P(t) = P₀ * e^(rt)
Where:
P(t) = population at time t
P₀ = initial population (current population = 70,000)
e = Euler's number (approximately 2.71828)
r = growth rate
t = time (in years)
First, let's find the growth rate (r). We know that the population doubles over 20 months, which is equivalent to 1.67 years (20/12 = 1.67). In exponential growth, the population doubles when the exponent (rt) is equal to ln(2) (the natural logarithm of 2), so:
ln(2) = rt
r = ln(2)/t
Substituting the values:
r = ln(2)/1.67
Next, we can calculate the population 5 years from now (t = 5):
P(t) = P₀ * e^(rt)
P(5) = 70,000 * e^((ln(2)/1.67) * 5)
Now, we can calculate the population using the given values.