A country's population in 1993 was 116 million.
In 2002 it was 121 million. Estimate
the population in 2007 using the exponential
growth formula. Round your answer to the
nearest million.
P = Aekt
124mil
121=116 e^k(2002-1993)
ln(121/116)=9k
solve for k.
Then
Population=116e^k(2007-1993)
To estimate the population in 2007 using the exponential growth formula, we need to determine the values of A, k, and t.
A represents the initial population, which was 116 million in 1993.
k represents the growth rate per year. To find k, we can use the formula:
k = ln(P2/P1) / (t2 - t1), where P2 is the population in 2002 (121 million), t2 is the year 2002, P1 is the population in 1993 (116 million), and t1 is the year 1993.
k = ln(121/116) / (2002 - 1993)
Do note that ln means natural logarithm, and we use it here because the exponential growth formula is based on continuous compounding.
t represents the number of years between the initial year (1993) and the target year (2007), which is 14 years (2007 - 1993).
Now, let's plug in the values and calculate k:
k = ln(121/116) / (2002 - 1993)
≈ 0.0144
Once we have the value of k, we can use the exponential growth formula to estimate the population in 2007:
P = A*e^(kt)
Plugging in the known values:
P = 116 * e^(0.0144 * 14)
Calculating this expression, we find:
P ≈ 131.84 million
Rounding this to the nearest million, the estimated population in 2007 using the exponential growth formula is 132 million.