The function f(x) = 200 × (1.098)x represents a village's population while it is growing at the rate of 9.8% per year

Question

Create a table to show the village's population at 0, 2, 4, 6, 8, and 10 years from now. Use your table to create a graph that represents the village's population growth. When the population doubles from its current size, the village will need to dig a new water well. To the nearest half of a year, about how long before it is time for the village to dig the new well?

Answer 1

x     |  f(x)=200(1.098^x)

-----|-------------------------

0    |  200

2    |  241.1208 ≅ 241

4    |  290.6962 ≅ 291

6    |  350.4645 ≅ 350

8    |  422.5214 ≅ 423

10  |  509.3935 ≅ 509

 

When the population doubles it will be at 400

 

400 = 200(1.098^x)

 

1.098^x = 2

Take log of both sides

log (1.098^x) = log 2

x[log 1.098] = log 2

x = (log 2)/(log 1.098)

 

x = 7.4141 years

 

Rounded to the nearest half a year the population

will double in 7 1/2 years.

 

Note that the value falls between the populations

on our value table of 6 years and 8 years so this

makes sense.

 

Graphing on this site really doesn't work well.  I

leave it to you to graph the values table for the

function.  You will need to label the axes in a

reasonable manner.  The horizontal axis, x = years,

I would simply label in even numbers 0, 2, 4, 6, 8, 10

and the vertical axis f(x) = population maybe in values

of 20 ..   starting from 200 ...  200, 220, 240, 260, ..., 520

or something similar.