The perimeter of the rectangular playground shown is 100 feet. What is the area of the playground?

Task 2 a. Do some research and find a city that has experienced population growth. Determine its population on January 1st of a

Galina-37 [17]

Exponential functions are functions defined by y = ab^x, where a represents the initial value, and b represents the rate

<h3>The equation of a city that has experienced a population growth</h3>

The initial population of the city is 10000, and the growth rate of the population is 4%.

So, the exponential equation is:

$y = 10000 * 1.04^x$

<h3>The equation of a city that has experienced a population decline</h3>

The initial population of the city is 12000, and the decay rate of the population is 3%.

So, the exponential equation is:

$y = 12000* 0.97^x$

<h3>The similarities in the equations</h3>

The similarity in both equations is that, they both represent exponential function.

<h3>The year the population of city A exceeds B</h3>

In (a) and (b), we have:

$y = 10000 * 1.04^x$ ---- city A

$y = 12000* 0.97^x$ --- city B

When city A exceeds city B, we have the following inequality

$10000 * 1.04^x > 12000 * 0.97^x$

Divide both sides by 10000

$1.04^x > 1.2 * 0.97^x$

Divide both sides by 0.97^x

$(\frac{1.04}{0.97})^x > 1.2$

$1.07^x > 1.2$

Take the natural logarithm of both sides

$\ln(1.07)^x > \ln(1.2)$

This gives

$x\ln(1.07) > \ln(1.2)$

Solve for x

$x > \frac{\ln(1.2)}{\ln(1.07)}$

$x > 2.69$

This means that, the population of city A will exceed city B after 3 years

<h3>The year the population of city A will be at least twice of city B</h3>

In (a) and (b), we have:

$y = 10000 * 1.04^x$ ---- city A

$y = 12000* 0.97^x$ --- city B

When city A is at least twice city B, we have the following inequality

$10000 * 1.04^x \ge 2 * 12000 * 0.97^x$

$10000 * 1.04^x \ge 24000 * 0.97^x$

Divide both sides by 10000

$1.04^x \ge 2.4 * 0.97^x$

Divide both sides by 0.97^x

$(\frac{1.04}{ 0.97})^x \ge 2.4$

$1.07^x \ge 2.4$

Take the natural logarithm of both sides

$\ln(1.07)^x \ge \ln(2.4)$

This gives

$x\ln(1.07) \ge \ln(2.4)$

Solve for x

$x\ge \frac{\ln(2.4)}{\ln(1.07) }$

$x\ge 12.9$

This means that, the population of city A will be at least twice city B after 13 years

Read more about exponential functions at:

brainly.com/question/11464095

3 0

3 years ago

I need help with A-G,I,L,N<br>I hope yall have a merry Christmas

KonstantinChe [14]

Format of my answer:

[Problem letter] Parallel Lines

- Converse / Reason

!! I am not sure which / what converses you are using, but I gave the reasoning for it. If you see something similar, use the converses you know !!

[a] j & k

- If two lines intersected by a transversal form congruent alternate interior angles, then the lines are parallel

[b] m & n

- If angles are supplementary in this placement, the lines are parallel

[c] l & n

- If angles are equal when they are corresponding, the lines are parallel

[d] l & m

- If two angles that are congruent are vertical, the lines are parallel

[e] j & k

- If two lines intersected by a transversal form congruent corresponding angles, then the lines are parallel

[f] l & n

- If angles are supplementary in this placement, the lines are parallel

[g] l & n

- If two angles that are congruent are vertical, the lines are parallel

[h] -------

[i] l & n

- If two angles that are congruent are vertical, the lines are parallel

[j] -------

[k] -------

[l] j & k

- If two lines intersected by a transversal form congruent corresponding angles, then the lines are parallel

[m] -------

[n] j & k

- If angles are supplementary in this placement, the lines are parallel

[o] -------

-> See attached for more information

Have a nice day! - hopefully these are mostly correct, been awhile since I've done this

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

6 0

2 years ago

Mountain officials want to know the length of a new ski lift from A to C , as shown in the figure below. They measure angle DAC

Ede4ka [16]

We assume that the hill is represented by points ACD and the ski lift is represented by points BCD. From the description above, points CDB would have an angle of 90 degrees. Then, we would have:

sin (32) = CD / 960
CD = 508.72

tan 32 = 508.72 / AD
AD = 814.13

Therefore, the distance would be 814.13 - 508.72 = 305.4 ft.

4 0

3 years ago

Plz help plz help plz help plz help plz help plz help plz help plz help plz help

Kay [80]

Answer:

a)1.41666667 b)705882353 / 1000000000

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

The area of a rectangle is 20. The length is 3 less than twice the width. Find the length and the width

SIZIF [17.4K]

The length of rectangle is 5 units and width is 4 units.

Step-by-step explanation:

Given,

Area of rectangle = 20

Width of rectangle = w

Length of rectangle = 2w-3

Area = Length * Width

$20=(2w-3)(w)\\20=2w^2-3w\\2w^2-3w-20=0$

Factorizing

$2w^2-8w+5w-20=0\\2w(w-4)+5(w-4)=0\\(2w+5)(w-4)=0$

Either;

2w+5=0 =>2w=-5

Or,

w-4 = 0 => w=4

As width cannot be negative, therefore,

width of rectangle = 4 units

length of rectangle = 2w-3 = 2(4)-3 = 8-3 = 5 units

The length of rectangle is 5 units and width is 4 units.

Keywords: area, rectangle

Learn more about rectangle at:

#LearnwithBrainly

3 0

3 years ago

The perimeter of the rectangular playground shown is 100 feet. What is the area of the​ playground?

The perimeter of the rectangular playground shown is 100 feet. What is the area of the playground?