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3 years ago

How many zeros are in f(x) = 3x^4 + x + 2

Mathematics

1 answer:

lana [24]3 years ago

6 0

Answer:

The power of the polynomial determines the number of zeroes it has in this case power is 4 so 4 zeroes. Whereas in 5^3+4 it has 3 zeroes as its power is 3. U can find the zero by trial and error method.

Hope this helps.

Step-by-step explanation:

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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

If < A and < B are vertical angles, and < A = 2x - 11 degrees, and < B = x + 7 degrees, find x.

Tema [17]

Answer:

x=18

Step-by-step explanation:

Vertical angles are congruent. This means that they are equal to each other. So, to solve set them equal to each other and isolate x. First, set up the equation. Then, subtract x from both sides. Finally, add 11 to both sides and simplify.

1) $2x-11=x+7$

2) $x-11=7$

3) $x=18$

7 0

3 years ago

75 days is how many months?<br><br>

Natali [406]

Well 2 months and 16 days

4 0

3 years ago

What is an equation of the line that passes through the points (2, -2) and (8, 4)?

WITCHER [35]

Answer:

HAVE YOU WATCHED OCTOPUS GAME

Step-by-step explanation:

5 0

2 years ago

Identify which of the following is most appropriate: discrete random variable, continuous random variable, or not a random varia

liraira [26]

Answer:

A.) Continuous random variable ;Not a random variable ; Discrete random Variable ; Continuous random variable ; discrete random variable

Step-by-step explanation:

Identify which is most appropriate category for the sample data given below :

a. Exact weights of the next 100 babies born in the United States

This is a continuous random varibake as it could take up any value including decimals in other to specify the exact weight of an individual.

b. Responses to the survey question "Which political party do you prefer?"

Not a random variable as the outcome to this question isn't numerical.

c. Numbers of spins of roulette wheels required to get the number 7

This is a discrete random variable as the number of roulette spins would be a whole number within a specified fic range.

d. Exact foot lengths of humans

Continuous random variable

The exact foot length of human would vary greatly and in a bid to give an exact value, foot length will most definitely take up decimal values

e. Shoe sizes (such as 8 or 8½) of humans.

This is also a discrete random variable as shoe sizes are restricted to a specific range. Even with the inclusion of 1/2 in the measurement, there are no values inbetween (8 and 8 1/2) which will be the same for the remaining value range.

5 0

2 years ago