Chapter 3.1, Problem 55E

Solution

To find: when was the population of city O 10 million.

Late in 1969

Given information:

The population of city O can be modeled by

  $P\left(t\right)=\frac{12.79}{1+2.402e^{-0.0309t}}$

where P is the population in millions and t is the number of years since April 1, 1900.

Property Used:

Product of power property:

  $a^{x+y}=a^x\cdot a^y$

Explanation:

The population of city O can be modeled by

  $P\left(t\right)=\frac{12.79}{1+2.402e^{-0.0309t}}$

Use the given model and substitute $P\left(t\right)=10$ and solve for t ,

  $10=\frac{12.79}{1+2.402e^{-0.0309t}}$

To solve this use the calculator. Graph both the equations $P\left(t\right)=\frac{12.79}{1+2.402e^{-0.0309t}}$ and $P\left(t\right)=10$ and use the intersect feature to find the required value of t .

First step is press and enter the equations as shown:

  

Now press and enter the values as shown:

  

Now press

  

Now pressand

  

Choose intersect option and press enter.

  

This gives $t=69.67$

So, the population of city O was 10 million in the year $1900+69.67=1969.67$ .

That is, in the late 1969’s the population was 10 million.