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Strike441 [17]
2 years ago
15

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.

Mathematics
1 answer:
AlexFokin [52]2 years ago
3 0

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.

<h3>How to graph a function?</h3>

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.

<h3>Calculation:</h3>

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

#SPJ1

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The volume of a right circular cone is 2,279.64 in cubed. If the height of the cone is 18 in, what is the diameter of the cone?
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ANSWER

A. 22 in

EXPLANATION

The volume of a cone is calculated using the formula:

Volume =  \frac{1}{3}  \times \pi {r}^{2} h

It was given that: the volume is 2,279.64 in³

The height of the cylinder is also given as: h=18 in.

We substitute, the given values into the formula to get:

2279.64=  \frac{1}{3}  \times (3.14) \times {r}^{2}  \times 18

2279.64= 18.84 {r}^{2}

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r = 11in

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Answer:

0.015625

Step-by-step explanation:

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100 pts help me please.
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<u>Answer:</u>

  • Carly's expenditure was $240 and the number of boxes of cards was required is 24 boxes.

<u>Step-by-step explanation:</u>

We know that:

  • 48 + 8(b) = Carly's expenditure
  • 10(b) = Carly's expenditure
  • 48 + 8b = 10b
  • B = Boxes of cards

<u>Work:</u>

  • 48 + 8b = 10b
  • => 48 + 8b - 8b = 10b - 8b
  • => 48 = 2b
  • => b = 24

<u>Now, let's substitute the value of b into any equation.</u>

  • 10(24)
  • => 240

<u>Hence, Carly's expenditure was $240 and the number of boxes of cards was required is 24 boxes.</u>

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