a countrys population in 1991 was 114 million in 1997 it was 120 million. estimate the population in 2014 using the exponential growth formula.
Let t be the number of years since 1991. Then we have
P(t) = 114 * (120/114)^(t/(1997-1991)
= 114 * 1.05263^(t/6)
Now find P(2014-1991) = P(23)
To estimate the population in 2014 using the exponential growth formula, we need to determine the growth rate (r) and use the formula: P = P0 * e^(r*t), where P is the population in the future (2014 in this case), P0 is the initial population (1991 in this case), e is the mathematical constant approximately equal to 2.71828, r is the growth rate, and t is the time duration in years.
First, let's calculate the growth rate (r). We can use the formula: r = ln(P1/P0) / t, where P1 is the final population (120 million in 1997 in this case), P0 is the initial population (114 million in 1991), and t is the time duration in years (1997 - 1991 = 6 years).
r = ln(120/114) / 6 ≈ 0.00993
Now, we can use the calculated growth rate (r) to estimate the population in 2014. The time duration from 1991 to 2014 is 23 years.
P = P0 * e^(r*t) = 114 * e^(0.00993 * 23)
Using a calculator or a computer program, we can calculate the value as:
P ≈ 166.43 million
Therefore, the estimated population in 2014 using the exponential growth formula is approximately 166.43 million.