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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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the length of a rectagle is 5 in longer than its width. if the perimeter of the rectangle is 58 in, find its length and width
dolphi86 [110]

Answer:

  • Length = 17 inches

  • Width = 12 inches

⠀

Step-by-step explanation:

⠀

As it is given that, the length of a rectangle is 5 in longer than its width and the perimeter of the rectangle is 58 in and we are to find the length and width of the rectangle. So,

⠀

Let us assume the width of the rectangle as x inches and therefore, the length will be (x + 5) inches .

⠀

Now, <u>According to the Question :</u>

⠀

{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}

⠀

{\longrightarrow \qquad { {\sf{2 ( x + 5 + x )= 58 }}}}

⠀

{\longrightarrow \qquad { {\sf{2 ( 2x + 5  )= 58 }}}}

⠀

{\longrightarrow \qquad { {\sf{ 4x + 10= 58 }}}}

⠀

{\longrightarrow \qquad { {\sf{ 4x = 58  - 10}}}}

⠀

{\longrightarrow \qquad { {\sf{ 4x = 48}}}}

⠀

{\longrightarrow \qquad { {\sf{ x =  \dfrac{48}{4} }}}}

⠀

{\longrightarrow \qquad{ \underline{ \boxed { \pmb{\mathfrak {x = 12}} }}} }\:  \:  \bigstar

⠀

Therefore,

  • The width of the rectangle is 12 inches .

⠀

Now, We are to find the length of the rectangle:

{\longrightarrow \qquad{ { \frak{\pmb{Length = x + 5 }}}}}

⠀

{\longrightarrow \qquad{ { \frak{\pmb{Length = 12 + 5 }}}}}

⠀

{\longrightarrow \qquad{ { \frak{\pmb{Length = 17}}}}}

⠀

Therefore,

  • The length of the rectangle is 17 inches .

⠀

8 0
1 year ago
Read 2 more answers
9. Evaluate 14(-6x +10) - 16x - 100x + 140 for x = -2.
Radda [10]

Answer:

680

Step-by-step explanation:

14(-6x +10) - 16x - 100x + 140 for x = -2.

14(-6(-2) + 10) - 16(-2) - 100(-2) + 140

14(12 + 10) + 32 + 200 + 140

14(22) + 372

308 + 372

680

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Step-by-step explanation:

the electromagnet lasts only as long as there is supply of electric current

4 0
3 years ago
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Pavlova-9 [17]

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Step-by-step explanation:

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The perimeter of a playing field for a certain sport is 242 ft. the field is a​ rectangle, and the length is 47 ft longer than t
Mariulka [41]
242-94 = 148 (length is 47 more than the width, you double the length to get the perimeter, so you double 47 which equals 94)
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4 0
3 years ago
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