Respuesta :
Population of New York City (in millions of people)
1997: 7.248
1998: 7.519
If we assume that the population of NYC grows exponentially, we can write this in functional form as:
[tex]P(y)=A\cdot b^y[/tex]Where A and b are parameters, and y is the number of years passed since 1997. P is the population in millions of people. Using the information above, the population of 1997 can be calculated for y = 0, and in 1998 by y = 1. Then:
[tex]\begin{gathered} P(0)=A\cdot b^0=7.248\Rightarrow A=7.248 \\ P(1)=A\cdot b^1=7.248\cdot b=7.519\Rightarrow b=\frac{7519}{7248} \end{gathered}[/tex]The expression is:
[tex]P(y)=7.248\cdot(\frac{7519}{7248})^y[/tex]The one-year growth factor is bš, and the two-year growth factor is b². This is:
[tex]\begin{gathered} 1\text{ year growth factor}\colon b^1=\frac{7519}{7248}\approx1.037 \\ 2\text{ year growth factor}\colon b^2=(\frac{7519}{7248})^2\approx1.076 \end{gathered}[/tex]The population of NYC in 2000 can be determined by multiplicating the population of NYC in 1998 by the 2 -year growth factor. This is:
[tex]2000\colon7.519\cdot b^2=8.092\text{ millions of people}[/tex]Finally, the 4-year growth factor is bâ´:
[tex]4\text{ year growth factor}\colon b^4=(\frac{7519}{7248})^4\approx1.158[/tex]