Question

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.

Answer 1

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.

How to graph a function?

For a function f(x) = y, the steps to draw a graph for the given function are as follows:

• Consider certain values of x
• Substitute x values in the given function to obtain y values
• Plot the x and y values in the graph
• Join the points to know the variation.

Calculation:

It is given that,

f(x) = 200 × $(1.098)^x$

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 × $(1.098)^0$ = 200

f(x = 2) = f(2) = 200 × $(1.098)^2$ = 241

f(x = 4) = f(4) = 200 × $(1.098)^4$ = 291

f(x = 6) = f(6) = 200 × $(1.098)^6$ = 350

f(x = 8) = f(8) = 200 × $(1.098)^8$ = 423

f(x = 10) = f(10) = 200 × $(1.098)^1^0$ = 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 × $(1.098)^t$

⇒ $(1.098)^t$ = 2

⇒ log$(1.098)^t$ = 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:

brainly.com/question/4025726

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