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alexira [117]
1 year ago
8

The population of a small town is decreasing exponentially at a rate of 14.3% each year. The current population is 9,400 people.

The town's tax status will change once the population is below 6,000 people.
Create an inequality that can be used to determine after how many years, t, the town's tax status will change, and use it to answer the question below.
Will the town's tax status change within the next 3 years?
Mathematics
1 answer:
KonstantinChe [14]1 year ago
7 0

Using an exponential function, the inequality is given as follows:

9400(0.857)^t < 6000

The solution is t > 2.9, hence the tax status will change within the next 3 years.

<h3>What is an exponential function?</h3>

A decaying exponential function is modeled by:

A(t) = A(0)(1 - r)^t

In which:

  • A(0) is the initial value.
  • r is the decay rate, as a decimal.

For this problem, the parameters are given as follows:

A(0) = 9400, r = 0.143.

The population after t years is modeled by:

A(t) = A(0)(1 - r)^t

A(t) = 9400(1 - 0.143)^t

A(t) = 9400(0.857)^t

The tax status will change when:

A(t) < 6000

Hence the inequality is:

9400(0.857)^t < 6000

Then:

(0.857)^t < \frac{6000}{9400}

\log{(0.857)^t} < \log{\left(\frac{6000}{9400}\right)}

t\log{0.857} < \log{\left(\frac{6000}{9400}\right)}

Since both logs are negative:

t > \frac{\log{\left(\frac{6000}{9400}\right)}}{\log{0.857}}

t > 2.9.

The solution is t > 2.9, hence the tax status will change within the next 3 years.

More can be learned about exponential functions at brainly.com/question/25537936

#SPJ1

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Answer:

10

Step-by-step explanation:

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|2+3(-4)|

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Now, subtract:

=|-10|

The absolute value of -10 is positive 10. So:

=10

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3 0
3 years ago
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Line RS intersects triangle BCD at two points and is parallel to segment DC. Triangle B C D is cut by line R S. Line R S goes th
Svetlanka [38]

Answer:

The correct options are;

1) ΔBCD is similar to ΔBSR

2) BR/RD = BS/SC

3) (BR)(SC) = (RD)(BS)

Step-by-step explanation:

1) Given that RS is parallel to DC, we have;

∠BDC = ∠BRS (Angles on the same side of transversal)

Similarly;

∠BCD = ∠BSR (Angles on the same side of transversal)

∠CBD = ∠CBD = (Reflexive property)

Therefore;

ΔBCD ~ ΔBSR Angle, Angle Angle (AAA) rule of congruency

2) Whereby  ΔBCD ~ ΔBSR, we therefore have;

BC/BS = BD/BR → (BS + SC)/BS = (BR + RD)/BR = 1 + SC/BS = RD/BR + 1

1 + SC/BS = 1 + RD/BR = SC/BS = 1 + BR/RD - 1

SC/BS = RD/BR

Inverting both sides

BR/RD = BS/SC

3) From BR/RD = BS/SC the above we have by cross multiplication;

BR/RD = BS/SC gives;

BR × SC = RD × BR → (BR)(SC) = (RD)(BR).

7 0
2 years ago
Anthony drove 765 miles in two days. At this rate, how many miles will he drive in 3.5 days
rosijanka [135]

Answer:

1,338.75 miles in 3.5 days.

Step-by-step explanation:

What I did was first, 765/2=382.5

Then I did 382.5x3.5=1338.75(rounded 1339 or 1340)

Hope this helps.

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2 years ago
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If f(x) = 2x + 5x and g(x) = 3x - 5, find (f+ g)(x).
Papessa [141]

Answer:

D. 10x - 5

General Formulas and Concepts:

<u>Algebra I</u>

  • Terms/Coefficients/Degrees

Step-by-step explanation:

<u>Step 1: Define</u>

f(x) = 2x + 5x

g(x) = 3x - 5

(f + g)(x) is f(x) + g(x)

<u>Step 2: Simplify</u>

f(x) = 7x

g(x) = 3x - 5

<u>Step 3: Find</u>

  1. Substitute:                     (f + g)(x) = 7x + (3x - 5)
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7 0
3 years ago
Use​ Newton's method to find an approximate solution of ln(x)=10-x. Start with x_0 =9 and find x_2 .
vova2212 [387]

Answer:

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Step-by-step explanation:

Given the function  ln(x)=10-x with initial value x₀ = 9, we are to find the second approximation value x₂ using the Newton's method. According to Newtons method xₙ₊₁ = xₙ -  f(xₙ)/f'(xₙ)

If f(x) = ln(x)+x-10

f'(x) = 1/x + 1

f(9) = ln9+9-10

f(9) = ln9- 1

f(9) = 2.1972 - 1

f(9) = 1.1972

f'(9) = 1/9 + 1

f'(9) = 10/9

f'(9) = 1.1111

x₁ = x₀ -  f(x₀)/f'(x₀)

x₁ = 9 -  1.1972/1.1111

x₁  = 9 - 1.0775

x₁  = 7.9225

x₂ = x₁ -  f(x₁)/f'(x₁)

x₂ = 7.9225 -  f(7.9225)/f'(7.9225)

f(7.9225) = ln7.9225 + 7.9225 -10

f(7.9225) = 2.0697 + 7.9225 -10

f(7.9225) = 0.0078

f'(7.9225) = 1/7.9225 + 1

f'(7.9225) = 0.1262+1

f'(7.9225) = 1.1262

x₂ = 7.9225 - 0.0078/1.1262

x₂ = 7.9225 - 0.006926

x₂ = 7.9156

<em>Hence the approximate value of x₂ is 7.9156</em>

7 0
3 years ago
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