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3 years ago

8

A train leaves chicago and travels east at 60 mph. another train at the same depot leaves at the same time and travels west at 7

2 mph. how long before the two trains are 330 miles apart?

1 answer:

charle [14.2K]3 years ago

8 0

Exactly 1 day 3 hours and 30 minutes,or 27.5 hours

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suppose you win a contest at the start of 9th grade that deposited $3000 in an account that pays 5% annual interest compound con

tiny-mole [99]

A=pe^rt
A=3,000×e^(0.05×8)
A=4,475.47

5 0

3 years ago

A. Do some research and find a city that has experienced population growth.

horrorfan [7]

A. The city we will use is Orlando, Florida, and we are going to examine its population growth from 2000 to 2010. According to the census the population of Orlando was 192,157 in 2000 and 238,300 in 2010. To examine this population growth period, we will use the standard population growth equation $N_{t} =N _{0}e^{rt}$
where:
$N(t)$ is the population after $t$ years
$N_{0}$ is the initial population
$t$ is the time in years
$r$ is the growth rate in decimal form
$e$ is the Euler's constant
We now for our investigation that $N(t)=238300$ , $N_{0} =192157$ , and $t=10$ ; lets replace those values in our equation to find $r$ :
$238300=192157e^{10r}$
$e^{10r} = \frac{238300}{192157}$
$ln(e^{10r} )=ln( \frac{238300}{192157} )$
$r= \frac{ln( \frac{238300}{192157}) }{10}$
$r=0.022$
Now lets multiply $r$ by 100% to obtain our growth rate as a percentage:
$(0.022)(100)$ =2.2%
We just show that Orlando's population has been growing at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.

B. Here we will examine the population decline of Detroit, Michigan over a period of ten years: 2000 to 2010.
Population in 2000: 951,307
Population in 2010: 713,777
We know from our investigation that $N(t)=713777$ , $N_{0} =951307$ , and $t=10$ . Just like before, lets replace those values into our equation to find $r$ :
$713777=951307e^{10r}$
$e^{10r} = \frac{713777}{951307}$
$ln(e^{10r} )=ln( \frac{713777}{951307} )$
$r= \frac{ln( \frac{713777}{951307}) }{10}$
$r=-0.029$
$(-0.029)(100)$ = -2.9%.
We just show that Detroit's population has been declining at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.

C. Final equation from point A: $N(t)=192157e^{0.022t}$ .
Final equation from point B: $N(t)=951307e^{-0.029t}$
Similarities: Both have an initial population and use the same Euler's constant.
Differences: In the equation from point A the exponent is positive, which means that the function is growing; whereas, in equation from point B the exponent is negative, which means that the functions is decaying.

D. To find the year in which the population of Orlando will exceed the population of Detroit, we are going equate both equations $N(t)=192157e^{0.022t}$ and $N(t)=951307e^{-0.029t}$ and solve for t:
$192157e^{0.022t} =951307e^{-0.029t}$
$\frac{192157e^{0.022t} }{951307e^{-0.029t} } =1$
$e^{0.051t} = \frac{951307}{192157}$
$ln(e^{0.051t})=ln( \frac{951307}{192157})$
$t= \frac{ln( \frac{951307}{192157}) }{0.051}$
$t=31.36$
We can conclude that if Orlando's population keeps growing at the same rate and Detroit's keeps declining at the same rate, after 31.36 years in May of 2031 Orlando's population will surpass Detroit's population.

E. Since we know that the population of Detroit as 2000 is 951307, twice that population will be $2(951307)=1902614$ . Now we can rewrite our equation as: $N(t)=1902614e^{-0.029t}$ . The last thing we need to do is equate our Orlando's population growth equation with this new one and solve for t:
$192157e^{0.022t} =1902614e^{-0.029t}$
$\frac{192157e^{0.022t} }{1902614e^{-0.029t} } =1$
$e^{0.051t} = \frac{1902614}{192157}$
$ln(e^{0.051t} )=ln( \frac{1902614}{192157} )$
$t= \frac{ln( \frac{1902614}{192157}) }{0.051}$
$t=44.95$
We can conclude that after 45 years in 2045 the population of Orlando will exceed twice the population of Detroit.

8 0

3 years ago

7 increased by 5 times a number ?

RideAnS [48]

Answer:

i wouldsay b

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Avery has 125 animal stickers. She gave 5 animal stickers to each of her 10 friends. HoW many animal stickers she have left? Wha

Angelina_Jolie [31]

Answer:

75

Step-by-step explanation:

125-(5*10)

125-(50)

75

3 0

3 years ago

Karley is an architect building the city pool. The larger rectangle represents the entire pool area. The smaller rectangle repre

Ahat [919]

Answer:

Area of the walkway border is 736 ft²

Step-by-step explanation:

A rectangle is a quadrilateral (has four sides and four angles) with two pairs of opposite and parallel sides. All angles in a rectangle are 90 degrees each. Also, opposite sides are equal.

The entire pool area has a length of 60 feet and width of 40 feet. The area of the entire pool area is:

Area of entire pool = length * width = 60 feet * 40 feet = 2400 ft²

The area of entire pool

A walkaway border of 4 ft is made around the pool area. There is a decrease of 4 ft round the sides of the pool area.

Therefore length of pool = length of entire pool area - 4 feet border at left - 4 feet border at right = 60 ft - 4 ft - 4 ft = 52 ft

width of pool = width of entire pool area - 4 feet border at top - 4 feet border at bottom = 40 ft - 4 ft - 4 ft = 32 ft

Therefore the pool is 52 ft × 32 ft

Area of pool = length * width = 52 ft * 32 ft = 1664 ft²

Area of the walkway border = Entire pool area - Area of pool = 2400 ft² - 1664 ft² = 736 ft²

8 0

3 years ago