You know the population of your nation was 151 million in 1990 and
173 million in 2000. Use the model f(t) = P e^rt to model your nation’s
population t years after 1990.
Using the correct rate of population growth, predict the year in
which your country’s population will finally reach 250 million.
well,
151e^(10r) = 173
e^(10r) = 173/151
r = ln(173/151) / 10 = 0.0136
To determine the rate of population growth, we can use the formula:
r = ln(P2/P1) / (t2 - t1)
Where:
P1 = initial population (151 million)
P2 = final population (250 million)
t1 = initial year (1990)
t2 = years after 1990 when the population reaches 250 million
r = growth rate
Substituting the given values into the formula:
r = ln(250/151) / (t2 - 1990)
Now, we can rearrange the formula to solve for t2:
(t2 - 1990) = ln(250/151) / r
Let's assume that the growth rate remains constant over the observed years. We'll use the population growth from 1990 to 2000 as an estimate for r:
r = ln(173/151) / (2000 - 1990)
r = ln(1.146) / 10
r ≈ 0.0393 (rounded to 4 decimal places)
Now we can substitute this value of r into the equation to solve for t2:
(t2 - 1990) = ln(250/151) / 0.0393
To find t2, we need to isolate it by moving the constant term to the other side:
t2 = (ln(250/151) / 0.0393) + 1990
Calculating this expression will give us the approximate year when the population will reach 250 million.