1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
Brainliest for help! <br> Sketch a graph of the function <br> y =sin(x) + 2
diamong [38]

Answer:

The parent sine graph y=sin(x) has a range of -1 ≤ y ≤ 1

It crosses the x-axis x = 0° ± 180°n

The maximum points occur when x = 90° ± 360°n and y = 1

The minimum points occur when x = 270° ± 360°n and y = -1

The sketch the graph of function y=sin(x)+2 we simply move the graph of y=sin(x) up 2 units.

So this means it will have a range of 1 ≤ y ≤ 3

It no longer crosses the x-axis.

The maximum points occur when x = 90° ± 360°n and y = 3

The minimum points occur when x = 270° ± 360°n and y = 1

<u>Attached diagram</u>

The parent function y=sin(x) is shown in grey (dashed line)

The function y=sin(x)+2 is shown in red.

4 0
2 years ago
Solve the system using elimination.
Shalnov [3]

Answer:

After simplifying we get (x,y) as (1,3).

Step-by-step explanation:

Given:

x+7y=22,

x-7y=-17

We need to use elimination method to solve the and simplify the equations.

Solution;

Let x+7y=22 ⇒ equation 1

Also Let 4x-7y=-17⇒ equation 2

Now by solving the equation we get;

first we will Add equation 2 from equation 1 we get;

(x+7y)+(4x-7y)=22+(-17)\\\\x+7y+4x-7y=22-17\\\\5x=5

Now Dividing  both side by 5 using division property of equality we get;

\frac{5x}{5}=\frac{5}{5}\\\\x=1

Now Substituting the vale of x in equation 1 we get;

x+7y=22\\\\1+7y=22

subtracting both side by 1 using subtraction property of equality we get;

1+7y-1=22-1\\\\7y=21

Now Dividing  both side by 7 using division property of equality we get;

\frac{7y}{7}=\frac{21}{7}\\\\y=3

Hence we can say that, After simplifying we get (x,y) as (1,3).

4 0
2 years ago
Choose the system of inequalities that best matches the graph below.
lapo4ka [179]

Answer:

D) y\:, y\:>\:-x

Step-by-step explanation:

The blue boundary line has a y-intercept of 2 and a slope of  2.

It has equation : y=2x+2

Since the boundary line is not solid and the lower half plane of this line is shaded, its inequality is

y\:

The blue boundary line passes through the origin and has slope -1.

Its equation is y=-x.

Since the boundary line is not solid and the right half-plane is shaded, its inequality is y\:>\:-x

The correct choice is D.

4 0
3 years ago
Suppose a computer technical support representative can answer calls from 8 customers in an hour. What is the probability that a
Ganezh [65]

Answer:

Option d

Step-by-step explanation:

We need 2 fundamental data to solve this problem.

1.- Average number of clients attended in 1 hour.

2.- Time in which it is expected that a client will be attended.

They tell us that the average number of clients served in an hour is m = 8

They tell us to calculate the probability that the client will be seen in less than 15 minutes.

But the time t in the formula is given in hours.

Therefore we must write 15 minutes according to hours.

We know that 1\ hour = 60 minutes.

So:

15\ minutes[\frac{1\ hour}{60\ minutes}] = 0.25\ hours.

Now we substitute in the formula m = 8 and t = 0.25 to find P.

P = 1 -e^{-mt}\\\\P = 1- e^{-(8)(0.25)}\\\\P = 1 - e^{-2}\\\\P = 0.8646\\\\P= 86\%

4 0
3 years ago
Read 2 more answers
Please help. I will give brainliest to correct answer.
Stells [14]

Answer:

The area of a square with side length of 2 inches is 4 square inches.

The area of a circle with radius 1.2 inches is:

\pi \times (1.2) ^{2}  \\  = 3.14 \times 1.44 \\  = 4.5216 \: square \: inches

That is approximately 4.5 square inches.

Hence, the area of the square (4) is less than {<} that of the circle (4.5)!

3 0
2 years ago
Other questions:
  • Imelda, Susan, and Clara are driving go-carts around a track. Imelda takes 14 minutes, Susan takes 18 minutes, and Clara takes 1
    14·1 answer
  • How to do multiplicities
    8·1 answer
  • Calculate the total surface area
    14·1 answer
  • A cone has a diameter of 12 ft and a slant height of 20 ft. Explain whether tripling both dimensions would triple the surface ar
    12·1 answer
  • AABC has vertices of A(-2, 2), B(-1, -2), C(-6, 1) and is translated right 7 and up 3.
    7·2 answers
  • Solve<br><br> 7x - 2 = 5x + 14
    9·1 answer
  • Random samples of size 64 are taken from an infinite population whose mean and standard deviation are 24 and 6.4, respectively.
    12·1 answer
  • On a standardized science test, the seniors at Fillmore High School have a mean score of 430 with a standard deviation of 90.
    10·1 answer
  • Please answer the questions
    9·1 answer
  • Helpppppppppp me plzz
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!