The time for the village to dig the new well is about 7 1/2 years. At this time the population doubles from its current size.
For a function f(x) = y, the steps to draw a graph for the given function are as follows:
It is given that,
f(x) = 200 × [tex](1.098)^x[/tex]
Village's population growing rate = 9.8%
Creating a table for x and f(x) values:
x: 0 2 4 6 8 10
f(x = 0) = f(0) = 200 × [tex](1.098)^0[/tex] = 200
f(x = 2) = f(2) = 200 × [tex](1.098)^2[/tex] = 241
f(x = 4) = f(4) = 200 × [tex](1.098)^4[/tex] = 291
f(x = 6) = f(6) = 200 × [tex](1.098)^6[/tex] = 350
f(x = 8) = f(8) = 200 × [tex](1.098)^8[/tex] = 423
f(x = 10) = f(10) = 200 × [tex](1.098)^1^0[/tex] = 509
So,
(x, f(x)): (0, 200) (2, 241) (4, 291) (6, 350) (8, 423) (10, 509)
Plotting these points in the graph and joining the points, the graph is shown below.
Finding the time for the village to dig a new well:
It is given that the population doubled from its current size, the village will need to dig new water well.
The current size of the village = 200
If it doubles for a certain time 't' = 400
So,
400 = 200 × [tex](1.098)^t[/tex]
⇒ [tex](1.098)^t[/tex] = 2
⇒ log[tex](1.098)^t[/tex] = log 2
⇒ t log(1.098) = 0.301
⇒ t × 0.04 = 0.301
∴ t = 7.525 years
Therefore, the village's population becomes double at the time 7 and half years from now. So, after 7 1/2 years, the village needs to dig a new well.
Learn more about the function and its graph here:
https://brainly.com/question/4025726
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