The population of a southern city follows the exponential law. If the population doubled in size over 28 months and the current population is 70 comma 000, what will the population be 4 years from now?
??? 70 comma 000 ??? are you kidding me? Why not type 70,000?
Anyway, since the population doubles every 28 months, then after x months,
P(x) = 70000 * 2^(x/28)
So, now just plug in x=48, which is how many months in 4 years, right?
To find the population 4 years from now, we need to understand the exponential growth function. The exponential growth formula can be written as:
P(t) = P(0) * e^(kt),
where:
P(t) = Population at time t,
P(0) = Initial population,
e = Euler's number (approximately 2.71828),
k = Growth rate constant,
t = Time in years.
We are given that the population doubled in size over 28 months. To find the growth rate constant (k), we can use the following equation:
P(t) = P(0) * e^(kt).
Let's rearrange the equation to solve for k:
2P(0) = P(0) * e^(k * (28/12)).
Dividing both sides by P(0) and taking the natural logarithm (ln) of both sides, we get:
ln(2) = k * (28/12).
Now we can solve for k:
k = ln(2) / (28/12).
Using the given current population of 70,000, we can substitute the values into the exponential growth function:
P(t) = 70,000 * e^[(ln(2) / (28/12)) * t].
To find the population 4 years from now, we substitute t = 4 into the equation:
P(4) = 70,000 * e^[(ln(2) / (28/12)) * 4].
Using a calculator, we can evaluate this expression to find the population 4 years from now.