Answer:
The value of f(3)=12.4
Step-by-step explanation:
Average rate of change = 3.4
Interval: -2 < x < 3
f(-2) = 9
We need to find f(3)
The formula used to calculate Average rate of change is: [tex]Average \ rate \ of \ change=\frac{f(b)-f(a)}{b-a}[/tex]
here we have a=-2 and b=3
Now finding f(3)
[tex]Average \ rate \ of \ change=\frac{f(b)-f(a)}{b-a}\\3.4=\frac{f(3)-f(-2)}{3-2} \\3.4=\frac{f(3)-9}{1}\\3.4=f(3)-9\\f(3)=3.4+9\\f(3)=12.4[/tex]
So, The value of f(3)=12.4
In 2012, the population of a city was 5.82 million. The exponential growth rate was 2.95% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be million?
d) Find the doubling time.
Answer:
a) P(t) = 6.57e ^{0.0287t}P(t)=6.57e
0.0287t
b) P(6) = 7,805\ millionP(6)=7,805 million
c) t = 14.64\ yearst=14.64 years
d) t = 24.15\ yearst=24.15 years
Step-by-step explanation:
a) The function of exponential growth for a population has the following formula:
P(t) = p_0e ^{rt}P(t)=p
0
e
rt
In this equation:
p_0p
0
is the initial population
r is the growth rate
t is the time in years
In this problem we know that
r = 2.87\% = 0.0287r=2.87%=0.0287
p_0= 6.57p
0
=6.57 million in the year 2012.
So the equation is:
P(t) = 6.57e ^{0.0287t}P(t)=6.57e
0.0287t
Where t = 0t=0 represents the year 2012
b) If t = 0t=0 in 2012, then in 2018 t = 6t=6
The population in 2018 is:
\begin{gathered}P(t = 6) = 6.57e ^{0.0287(6)}\\\\P(6) = 7,805\ million\end{gathered}
P(t=6)=6.57e
0.0287(6)
P(6)=7,805 million
c) To know when the population is equal to 10 million we must equal P(t) to 10 and solve for t.
\begin{gathered}P(t) = 10 = 6.57e ^{0.0287t}\\\\\frac{10}{6.57} = e ^{0.0287t}\\\\ln(\frac{10}{6.57}) = 0.0287t\\\\t = \frac{ln(\frac{10}{6.57})}{0.0287}\end{gathered}
P(t)=10=6.57e
0.0287t
6.57
10
=e
0.0287t
ln(
6.57
10
)=0.0287t
t=
0.0287
ln(
6.57
10
)
t = 14.64\ yearst=14.64 years
d) The function is doubled when P(t) = 2p_0P(t)=2p
0
P(t) = 2(6.57) = 13.14 = 6.57e ^{0.0287t}P(t)=2(6.57)=13.14=6.57e
0.0287t
We solve for t.
\begin{gathered}\frac{13.14}{6.57} = e ^{0.0287t}\\\\ln(\frac{13.14}{6.57}) = 0.0287t\\\\t = ln{13.14}{6.57})}{0.0287})\
end
{gathered}
6.57
13.14
=e
0.0287t
ln(
6.57
13.14
)=0.0287t
t=
0.0287
ln(
6.57
13.14
)
)
t = 24.15\ yearst=24.15 years
Find a degree 3 polynomial having zeros -1,2 and 7 and the coefficient of x^3 equal 1.
Answer:
[tex]x^{3}-8x^{2} +5x+14[/tex]
Step-by-step explanation:
n=3
f(x) = (x-(-1))(x-2)(x-7)
=(x+1)(x-2)= [tex](x^{2} -x-2)[/tex](x-7)=[tex]x^{3}-8x^{2}+5x+14[/tex]
what expression gives the solution to -5+2x^2=-6x
Answer:
Step-by-step explanation:
2x² + 6x - 5 = 0
D = 36 + 40 = 76 = (2√19)²
[tex]x_{1}[/tex] = ( - 6 - 2√19) / 4 = ( - 3 - √19) / 2
[tex]x_{2}[/tex] = ( - 3 + √19) / 2
If g(x) = -2x+4 and h(x)= -4x -5, find g(3)-h(5)
Answer:
3g−5h
Step-by-step explanation:
i just used a calculator lol but i wanted to help still
Answer:
3g-5h
Step-by-step explanation:
a proportional relationship is represented on a graph with a line that has a slope of 40 what is the unit rate
Answer:40
Step-by-step explanation:
Write and solve an equation to find the value of x. PLS HELP!!
Answer:
23.59 - 14.89 = x
x = 8.7
Step-by-step explanation:
To find x, you need to add all of the other sides and subtract it from the perimeter. 5.62 + 5.62 + 3.65 = 14.89.
23.59 - 14.89 = x, so x = 8.7
Answer:
8.7
Step-by-step explanation:
Add all the numbers together (5.62, 5.62, and 3.65) then take away from the result (23.59) to get answer.
Alex placed a classified ad in the local newspaper to sell his used Nissan Sentra. He plans to write a 9 line ad. The newspaper charges $17.50 for the first three lines (total) and then $8.25 for each extra line. How much will Alex pay for the ad?
Answer:
$67 total
Step-by-step explanation:
9-3= 6
6(8.25)= 49.50
49.50+17.50= $67
Answer:
$67.00
Step-by-step explanation
17.50 (first 3 lines) + 8.25 (for each of the 6 lines left)
17.50 + (8.25*6) =
17.50 + 49.50 =
67
The number 1,645.6 expressed in scientific notation equals
Answer:
[tex]1.6456 * 10^{3}[/tex]
Step-by-step explanation:
Step 1: Convert to Scientific Notation
[tex]1645.6[/tex] is in standard notation
[tex]1.6456 * 10^{3}[/tex] is in scientific notation
Answer: [tex]1.6456 * 10^{3}[/tex]
Travis made a business trip of
195.5 miles. He averaged
53 mph for the first part of the trip and
58 mph for the second part. If the trip took
3.5 hours, how long did he travel at each rate?
Answer:
At 53 mph, he traveled for 1.5 hours
At 58 mph, he traveled for 2 hours
Step-by-step explanation:
Mathematically;
distance = speed * time
let the time for the first part of the trip be x hours and the second part be y hours
Total hours is 3.5
So therefore;
x + y = 3.5 ••••••••(i)
Now let’s work with the rate
53 mph for x hours = 53 * x = 53x miles
58 mph for y hours = 58 * y = 58y miles
Adding both;
53x + 58y = 195.5 miles ••••••••(ii)
We have two equations to solve simultaneously
From i, x = 3.5 - y
insert into ii
53(3.5-y) + 58y = 195.5
185.5 - 53y + 58y = 195.5
5y = 195.5-185.5
5y = 10
y = 10/5
y = 2 hours
x = 3.5 - y
x = 3.5 - 2
x = 1.5 hours
the question is the picture
Answer:
1/5x
Step-by-step explanation:
A gradient is another word for slope.
every 4 minutes the volume increases by 20
so = rise/run = 4/20
now reduce
4/20
2/10
1/5
Rewrite in radical form
Answer:
6 1/3
Step-by-step explanation:
Selena has a piece of ribbon that is 130 inches long. If she wants to make bracelets that are 9 inches long, how many inches of ribbon will be left over?
Answer:14 4/9
Step-by-step explanation:
Please help please help,! :( this is urgent!
Answer: A
Step-by-step explanation:You are painting a 1/3 of a 1/4 so it's A
PLEASE HELP ME Jimmy's school is selling tickets to the annual talent show. On the day of ticket sales the school sold 4 adult tickets and 6 child Tickets for a total of $80 the school took and 24 on the second day by selling for adult tickets and seven child tickets find the price of an adult ticket and the price of a child ticket
Answer:
what is the OBJOBJ thing? wtheck
Step-by-step explanation:
there are 60student in a class there fourths of the. are girls how many boys are there
WILL GIVE BRAINLIEST! Which is a Proportional Relationship?
Equation A- y= [tex]\frac{5}{x} y{2}[/tex]
Equation B- y= [tex]x^{3}[/tex]
Equation C- y= 2x- 5
Equation D- y= [tex]\frac{x}{7}[/tex]
Answer:
the answer is y= x/7
Answer:
its D
Step-by-step explanation:
u should be able to mark him brainliest now
An account is opened with an initial deposit of $700 and earns 3.3% interest compounded semi-annually. What will the account be worth in 3 years? Round your answer to the nearest cent.
Answer:
772.22
Step-by-step explanation:
A=$700(1+0.0332)2(3). Simplify using the order of operations: A=$700(1.0165)6=$700(1.103174712)≈$772.22.
Six plus five times a number is more than the
number plus eight. Write an inequality and
solve it.
Answer:
x > 0.5
Step-by-step explanation:
Let the number be x.
6 + 5x > x + 8
4x > 2
x > 0.5
This is a question on inequalities. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)
Which of the following terms best describes three points that all lie in a
straight line?
A. Collinear
B. Congruent
C. Midpoint
D.equal
Answer:
A.
Explanation:
Collinear
The required term is "collinear" which best describes three points that all lie in a straight line. which is the correct answer would be an option (A).
What are the collinear points?Collinear points are locations along a straight line that are represented by a collinear. They are always collinear since a straight line may be traced continuously between any two places. A collinear connection can exist between three or more points, but it is not required. The word required is "collinear," which best depicts three locations that are all in a straight line.
Therefore, the required term is "collinear" which best describes three points that all lie in a straight line.
Hence, the correct answer would be option (A).
Learn more about the collinear points here:
brainly.com/question/5191807
#SPJ2
IX+XC= WHAT IS THE ANSWER
Answer: X googled it
This converts to the number 99
=========================================================
Explanation:
The upper case letter i means the number 1 in roman numerals. The X represents 10. The C represents 100.
I = 1
X = 10
C = 100
When we form something like IX, we have the smaller digit first and then a larger digit next. Whenever this happens, we subtract
IX = 10-1 = 9
Similarly
XC = 100-10 = 90
So we can see that
IX + XC = 9 + 90 = 99
---------------------------
Since XC is larger than IX, we list XC first when it comes to adding
In other words, we need to write IX+XC as XC+IX which collapses to XCIX
Placing XC next to IX without a plus sign implies the plus sign is there. This is effectively how roman numerals work (they are additive)
So,
XCIX = XC+IX = 90+9 = 99
Note how the XC takes care of the tens digit while IX takes care of the units digit.
Which table represents a linear function? Thanks! :)
Answer:
the first table
Step-by-step explanation:
Answer:
the first table
Step-by-step explanation:
this was on edjednuty
what i the answer and why this is for my little brother
Answer:
C, 1 1/14
Step-by-step explanation:
You would convert 1/2 to 7/14 and convert 4/7 to 8/14. You can now add them together, and once you do you get 15/14. You can now simplify, giving you your answer of 1 1/14.
The police in a certain city are investigating whether the proportion of minor traffic accidents is greater on Friday nights than on Saturday nights
Counting up on a number line starting at 0 corresponds with what numbers
Isabel company offers other programs and incentives to help employees with their savings and expenses.
Answer:
dependent care FSA
Health FSA
IRA
Step-by-step explanation:
Determine the sample size required to estimate the mean score on a standardized test within 4 points of the true mean with 98% confidence. Assume that s = 15 based on earlier studies.
Answer:
67
Step-by-step explanation:
You have to use fractions to show your work and I'm not going to do that but just know that it is the answer.
| 3x + 2 |= 4x + 5
explain how to solve it please
Answer:
x = -3
Step-by-step explanation:
Subtract 2 from both sides of the equation.
3x + 2 = 4x + 5
3x + 2 - 2 = 4x + 5 - 2
Step 2.
Simplify. Subtract the numbers 3x =4x + 3
Now subtract 4 from both sides.
Combine like terms -x = 3
Divide both sides of the equation.
Cancel terms that are in both the numerator and denominator
Divide the numbers
And that's how X = -3
Hope this helped you! If it did, please mark as brainliest this helps me and others a lot. Have a wonderful day.
what is 1 and 1/4 divided by 1 and 2/5
Answer:
25/28
Step-by-step explanation:
How do you do these questions?
Answer:
k = 0.2
A = (M / P₀) − 1
Step-by-step explanation:
dP/dt = kP
When t = 0, P = 1000 and dP/dt = 200.
200 = 1000k
k = 0.2
P = M / (1 + Ae⁻ᵏᵗ)
When t = 0, P = P₀.
P₀ = M / (1 + A)
1 + A = M / P₀
A = (M / P₀) − 1
Seven out of ten people say they will vote for Mrs. Meekus . If 5,500 people vote,how many are likely to vote for Mrs.Meekus
Answer:
3,850 people are likely to vote for Mrs. Meekus.
Step-by-step explanation:
Given that Mrs. Meekus has a voting intention of 7 out of 10, that is, 70%, in the event that 5,500 people are going to vote in the elections, the voting intention for this candidate would be obtained through the following calculation:
5,500 x 0.70 = X
3,850 = X
Thus, if said voting intention is reproduced, Mrs. Meekus would be voted by 3,850 voters.