1. What is the average rate of change of the function f(x)=5(2)^x from x = 1 to x = 5?

What is the slope of the line that passes through the points (3, -2) and (9, -2)?

solniwko [45]

Answer:

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Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Jared‘s grandmother gave him $19 for his birthday he brought eight dollars worth of candy and spent another four dollars on a ne

cestrela7 [59]

Answer:

$7

Step-by-step explanation:

To solve this one we will subtract how much he spends from what he has. At the start he had 19 and then spent 8 meaning he now has 8 less than when we started so 19-8 is 11. He now as 11 dollars, then he spend another 4 meaning we have to subtract another 4 dollars. 11-4 is 7. So he as 7 dollars left at the end.

I hope this helps and please don't hesitate to ask if there is anything still unclear!

7 0

3 years ago

Read 2 more answers

Use the following frequency distribution (of SAMPLE DATA) in answering the questions: class 0-9 f=10; class 10-19 f=20; class 20

lutik1710 [3]

Answer:

1. Five classes in the frequency distribution

2.The mid point of the third class is 24.5

3.The total number of frequency is 100

4.The relative frequency of the third class is (20/100=0.2)

5. We use n-1 because we are dealing with a sample data

6. The mean is 24.5

7. The value of the standard deviation is 11

Step-by-step explanation:

See attached picture for the solutions

4 0

3 years ago

HURRY PLEASE HELP ME? <br> WiLL GIvE brainliest.

solniwko [45]

Subtitute the pair (3,28) to x and y, if the result in right side is -8, then the pair is a solution to the equation

2x - y/2
= 2(3) - 28/2
= 6 - 14
= -8

The result is -8, so the pair (3,28) is a solution

3 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

4 years ago