Answer
$P(t)=\displaystyle \frac{4500}{1+1.176(1.0363)^{-t}}$
Population will reach 4 million in $2013.$
Work Step by Step
(We use desmos.com for the calculations/graph below.)
Logistic Model form: $\displaystyle \quad P=\frac{N}{1+Ab^{-t}}$
1. create a table with variable names $t$ and $P$ and enter the data.
2. in the next free cell, enter
$P\sim 4500/(1+Ab^{-t})$
(we assume the level-off value is 4.5 million)
The calculator returns $\left\{\begin{array}{l}
A=1.1760\\
b=1.0363
\end{array}\right.$
(rounded to 4 decimal places.)
3. since we have the graph of the logistic model, enter the equation $y=4000$ into the next empty cell.
Reading the intersection point $(62.868,4000)$, we interpret:
About 63 years after 1950, the population will be $4$ million.
