Could someone help me figure this out please? I have attached the problem (jpg). If you would like to know the answer lmk. Thanks
Hello, Sprinkledozer!
A telephone company estimates that the number N of phone calls per day
between two cities of population $\displaystyle P_1$ and $\displaystyle P_2$ that are $\displaystyle d$ miles apart is given by:
. . $\displaystyle N \:=\:\frac{2.51P_1P_2}{d^2}$
115. Estimate the population $\displaystyle (P_1)$ of a city given that
. . . . . the population of a second city is: $\displaystyle P_2 = 48,\!000$,
. . . . . the number of phone calls per day is: $\displaystyle N = 1,\!100,\!000$,
. . . . . and the distance between the cities is: $\displaystyle d=75$ miles.
. . . Round to the nearest thousand.
First, solve for $\displaystyle P_1.$
We have: .$\displaystyle \frac{2.51P_1P_2}{d^2} \:=\:N$
Multiply by $\displaystyle d^2\!:\;\;2.51P_1P_2 \:=\:d^2N $
Divide by $\displaystyle 2.51P_2\!:\;\;P_1 \;=\;\frac{d^2N}{2.51P_2}$
Substitute: .$\displaystyle P_1 \;=\;\frac{75^2(1,\!100,\!000)}{2.51(48,\!000)} \;=\;51,357.07171$
Therefore: .$\displaystyle P_1 \;\approx\;51,\!000$