Need help with these problem, I really need help, thanks.

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

Would anyone help With these questions it's the last one I don't know how to do them 1,2,3,4,5 and 6

Shtirlitz [24]

Answer:

See below

Step-by-step explanation:

1. Use x to designate the number of hours worked.

Plumber 1 = 35(x) + 25

Plumber 2 = 40(x)

Now you need to find when these two equations are equal to each other.

35(x) + 25 = 40(x)

Solve for x.

25 = 40x - 35x

25 = 5x

5 = x

So when the service call equals 5 hours, both plumbers will charge the same amount of money.

2. Use x to designate the number of months.

Center 1 = 30x

Center 2 = 22x + 80 initiation fee

Now you need to make the two equations equal to each other and solve for x.

30x = 22x + 80

30x - 22x = 80 or 8x = 80

x = 10 months

3. Use x to designate the pounds of the package

Shipper 1 = 14 + 2x

Shipper 2 = 20 + 1.5x

Make the two equations equal to each other.

14 + 2x = 20 + 1.5x

2x - 1.5x = 20 - 14

0.5x = 6

x = 12 pounds

4. Deanna $15 using $0.75 per game. This means she can play a total of 20 games before having $0.

Lise $13 using $0.50 per game. This means she can play a total of 26 games before having $0.

So since both end up with $0, you can see that Deanna would play 20 games and Lise would play 26 games.

5. Use x to designate the call time length.

Hotel 1 = 1 + 0.80x

Hotel 2 = 2 + 0.75x

Make both equations equal to each other.

1 + 0.8x = 2 + 0.75x

0.8x - 0.75x = 2 - 1

0.05x = 1

x = 20

6. Use x to designate semesters.

Duke = 22 + 6x

Kila = 4 + 12x

22 + 6x = 4 + 12x

22 - 4 = 12x - 6x

18 = 6x

3 = x semesters

6 0

3 years ago

Write all prime numbers from 20 to 50.

givi [52]

Answer:

So, 23, 29, 31, 37, 41, 43 and 47 these are the prime numbers between 20 and 50.

Step-by-step explanation:

plz mark me brainliest

5 0

3 years ago

Read 2 more answers

Sabrina ' car used 12 gallons of gas to travel 456 miles. How many miles did her car travel per

Darya [45]

You would divide 456 miles by the number of gallons used to get the answer of 38 miles per gallon.

5 0

3 years ago

Can someone help me in probability?

Afina-wow [57]

The probability is a fraction. all possible outcomes / number of items
so 8/11 is the probablity of finding a number higher than 3 out of 11
could also be written as:
8/11
8:11
.73
73 percent

8 0

4 years ago