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musickatia [10]
3 years ago
8

The population of a town is 13,000. It decreases at a rate of 5% per year. In about how many years will the population be less t

han 12,000?
Mathematics
1 answer:
just olya [345]3 years ago
3 0

This is an exponential decay problem.

Using the equation Y = a *(1-rate)^time

where Y is the future value given as 12,000 and a is the starting value given as 13,000.

The rate is also given as 5%.

The equation becomes:

12,000 = 13,000(1-0.05)^x

12,000 = 13,000(0.95)^x

Divide each side by 13000:

12000/13000 = 0.95^x/13000

12/13 = 0.95^x

Use the natural log function:

x = ln(12/13) / ln(0.95)

x = 1.56 years. ( this will equal 12,000

Round to 2 years it will be less than 12000.

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In which function does an increase of 1 in quantity x correspond to an increase of 8 in
OLga [1]

Answer:

C. y = 8x

Step-by-step explanation:

When x = 1

y = 8(1) = 8

when x = 2

y = 8(2) = 16

x increased by 1

y increased by 8

8 0
2 years ago
Use the given information to find the unknown value:y varies inversely with a. When x = 4, then y= 4. Find y when I = 2.Iyy =hel
Mashutka [201]

Inverse variation:

y=\frac{k}{x}

k is a constant

Use the given information (when x=4 y=4) to find the value of the constant:

\begin{gathered} 4=\frac{k}{4} \\  \\ \text{Multiply both sides of the equation by 4:} \\ 4\times4=4\times\frac{k}{4} \\  \\ 16=k \\  \\  \\ k=16 \end{gathered}

Then, the given relationship has the next equation:

y=\frac{16}{x}

Use the equation above to find y when x=2:

\begin{gathered} y=\frac{16}{2} \\  \\ y=8 \end{gathered}Then, when x=2, y=8
3 0
1 year ago
The mean age of 5 people in a room is 28 years.
lina2011 [118]

Answer:

174

Step-by-step explanation:

You should look at the mean and do this:

5*28 so now you know all the ages which is 140 now you do 140/29 and you get 4.8....... so you  can see that the answer is 174

4 0
3 years ago
What is the slope of the line through the points (0, 0) and (2, 6)
EleoNora [17]
For this problem, you would use the slope formula, or m=(y2-y1)/(x2-x1). So, let's put in what we know.

The x's and y's correspond with our coordinates. So let's plug that in:

m=(6-0)/(2-0)
m=(6)/(2)
m=3

So, the slope of your line is 3.
6 0
3 years ago
X, Y, and Z are collinear and Y is between X and Z. If XY = 3x – 1, YZ = 5, and XZ = 5x – 8,
salantis [7]

Answer:

6

Step-by-step explanation:

XY = 3x – 1, YZ = 5, and XZ = 5x – 8,

We know that XY + YZ = XZ, so

3x - 1 + 5 = 5x - 8

3x + 4 = 5x - 8

3x + 12 = 5x

12 = 2x

6 = x

4 0
2 years ago
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