Question

MEDAL & FAN :DD
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.

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

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


Create a table to show the village's population at 0, 2, 4, 6, 8, and 10 years from now.


x = 0


f(0) = 200*(1.098)^0


f(0) = 1


x = 2


f(2) = 200*(1.098)^2


f(2) = 241.1208


x = 4


f(4) = 200*(1.098)^4


f(4) = 290.6962


x = 6


f(6) = 350.4645


x = 8


f(8) = 425.5214


x = 10


f(10) = 509.3935
when the population doubles f(x) = 2*200 = 400, lets find x


200*(1.098)^x = 400


by solving we find


x = 7.5 years

Answer 2

@nathshely