Problema Solution
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 provided by our tutors
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
Use your table to create a graph that represents the village's population growth.
click here to see the graph of the function
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?
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
click here to see the step by step solution of the equation
the village will need to dig a new well in 7.5 years time.