Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The mayor of Brookmarsh is running a campaign to revitalize his city. Currently, the population of Brookmarsh is 10,000 and is increasing at a rate of
2% per year. The mayor predicts that the population will continue to grow in this manner, and that in
t years, the population will be at least 15,000 .
Write an inequality in terms of
t that models the situation.

The mayor of Brookmarsh is running a campaign to revitalize his city. Currently, the population of Brookmarsh is $10$ , $000$ and is increasing at a rate of $2 \%$ per year. The mayor predicts that the population will continue to grow in this manner, and that in $t$ years, the population will be at least $15$ , $000$ . $\newline$ Write an inequality in terms of $t$ that models the situation.

View step-by-step help

View step-by-step help

Write a linear inequality: word problems

Full solution

Q. The mayor of Brookmarsh is running a campaign to revitalize his city. Currently, the population of Brookmarsh is

10

,

000

and is increasing at a rate of

2 \%

per year. The mayor predicts that the population will continue to grow in this manner, and that in

t

years, the population will be at least

15

,

000

.

\newline

Write an inequality in terms of

t

that models the situation.

Identify Population and Growth Rate: Identify the initial population and the growth rate. $\newline$ The initial population of Brookmarsh is $10,000$ , and it is increasing at a rate of $2\%$ per year.
Express Growth Mathematically: Express the population growth mathematically. The population after $t$ years can be modeled by the equation $P(t) = P_0 \times (1 + r)^t$ , where $P_0$ is the initial population, $r$ is the growth rate, and $t$ is the number of years.
Substitute Given Values: Substitute the given values into the equation. $\newline$ For Brookmarsh, $P_0 = 10,000$ and $r = 2\%$ or $0.02$ . So the equation becomes $P(t) = 10,000 \times (1 + 0.02)^t$ .
Write Prediction Inequality: Write the inequality that represents the mayor's prediction. $\newline$ The mayor predicts that the population will be at least $15,000$ . So the inequality is $P(t) \geq 15,000$ .
Substitute Growth Equation: Substitute the population growth equation into the inequality. $\newline$ Replace $P(t)$ with the expression from Step $3$ to get $10,000 \times (1 + 0.02)^t \geq 15,000$ .

More problems from Write a linear inequality: word problems

Question

s

\newline

|s| + 3 \geq 8

Posted 4 months ago

Question

Which compound inequality represents the value of

x ?

\newline

(x - 1)(x + 1) > 0

\newline

Posted 4 months ago

Question

A particular company charges advertisers a one time cost of

\$500

, in addition to

\$4.50

for every one thousand times an advertisement is shown on the company's webpage. An advertiser wants its ad to appear

M

thousand times on the webpage, but does not want to spend more than

\$5,000

. Which of the following inequalities best describes the situation?

\newline

\newline

500+4.50M\geq5,000

\newline

4.50+500M>5,000

\newline

500+4.50M\leq5,000

\newline

500+4.50M<5,000

Posted 7 months ago

Question

7x+1 < x+9

\newline

Which of the following best describes the solutions to the inequality shown?

\newline

1

\newline

x > \frac{4}{3}

\newline

x < \frac{4}{3}

\newline

x < 1

\newline

x < \frac{5}{3}

Posted 4 months ago

Question

52-3x < -14

\newline

Which of the following best describes the solutions to the inequality shown?

\newline

1

\newline

x > -\frac{38}{3}

\newline

x > \frac{38}{3}

\newline

x < 22

\newline

x > 22

Posted 10 months ago

Question

5-3x > 2x+2

\newline

Which of the following best describes the solutions to the inequality shown?

\newline

1

\newline

x < \frac{7}{5}

\newline

x < 3

\newline

x < \frac{3}{5}

\newline

x > \frac{3}{5}

Posted 10 months ago

Question

Rani is a real estate agent. For each house she sells, she pays

\$ 100

in fees, but earns a commission of

1.8 \%

of the selling price of the house. Rani's total profit from a particular house is

\$ 4,580

p

represents the selling price of the house, which equation best models the situation?

\newline

1

\newline

0.018 p-100=4580

\newline

0.018 p+100=4580

\newline

(100-0.018) p=4580

\newline

(100+0.018) p=4580

Posted 8 months ago

Question

A commercial airplane that is

1

500

2

500

-mile journey is traveling at

450

knots in still air when it picks up a tailwind of

150

knots (in the same direction). If

h

is the number of hours remaining in the airplane's flight, which of the following equations best describes the situation?

\newline

1

\mathrm{knot}=1.15

miles per hour (mph)

\newline

1

\newline

1,500+690 h=2,500

\newline

1,500+600 h=2,500

\newline

1,500-600 h=2,500

\newline

1,500-690 h=2,500

Posted 7 months ago

Question

A weeping willow that is

15

feet in height grows to a maximum height of

35

y

years at a constant rate of

24

inches per year. Which of the following equations best describes this situation?

\newline

1

=12

\newline

1

\newline

35=15+2 y

\newline

35=15+24 y

\newline

35=15-2 y

\newline

35=15-24 y

Posted 10 months ago

Question

The gas mileage for a car is

23

miles per gallon when the car travels at

60

miles per hour. The car begins a trip with

13

gallons in its tank, travels at an average speed of

60

miles per hour for

h

hours, and ends the trip with

10

gallons in its tank. Which of the following equations best models this situation?

\newline

1

\newline

13-\frac{23 h}{60}=10

\newline

13-\frac{60 h}{23}=10

\newline

\frac{13-60 h}{23}=10

\newline

\frac{13-23 h}{60}=10

Posted 8 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant