Answer:
a) The exponential growth function
P(t) = 5,690,000(1.0287)^t
b) 6,742,868.7374 million
c) 12.04 years
d) 2439.0243902
Step-by-step explanation:
In 2012, the population of a city was 5.69 million. The exponential growth rate was 2.87% per year.
The formula for exponential growth is given as:
P(t) = Po( 1 + r) ^t
Where P = Population size after time t
Po = Initial population size
r = Growth rate in percentage
t= time in years
a) Find the exponential growth function.
P(t) = Population size after time t
Po = Initial population size = 5.69 million
r = Growth rate in percentage = 2.87% = 0.0287
t= time in years
The Exponential growth function
P(t) = 5,690,000(1 + 0.0287)^t
P(t) = 5,690,000(1.0287)^t
b) Estimate the population of the city in 2018.
From 2012 to 2018 = 6 years
t = 6 years
Hence,
P(t) = Po( 1 + r) ^t
P(t) = 5,690,000(1 + 0.0287)^6
P(t) = 5,690,000(1.0287)^6
P(t) = 6,742,868.7374 million
c) When will the population of the city be 8 million?
P(t) = 8,000,000
P(t) = Po( 1 + r) ^t
P(t) = 5,690,000(1 + 0.0287)^t
8,000,000 = 5,690,000(1 + 0.0287)^t
8,000,000 = 5,690,000(1.0287)^t
Divide both sides by 5,690,000
8,000,00/5,690,000 = 5,690,000(1.0287)^t/5,690,000
= 1.4059753954 = 1.0287^t
Take logarithm of both sides
log 1.4059753954 = log 1.0287^t
Log 1.4059753954 =t Log 1.0287
t = Log 1.4059753954/Log 1.0287
t = 12.041740264
t = 12.04 years
d) Find the doubling time.
The formula is given as 70/Growth rate
= 70/0.0287
= 2439.0243902
Interpreting Expressions
Breanna thought of a number, added 5 to it, and then multiplied her answer by 3. She got a final number of 21. What was her starting number?
Answer:
r u going to be a little late to the party but I
200x52-77=
please answer correct
Round 347−−−√ to the nearest hundredth.
Answer:300
Step-by-step explanation:
Samuel orders four DVD's from an online music store. Each DVD costs $9.99. He has a 20% discount code and sales tax is 6.75%. What is the total cost of his order? Please helpppp
What appears to be the range of the part of the function shown on the grid?
(A) g(x) = 2x
(B) g(x) = x - 3
(C) g(x) = x - 8
(D) g(x) = 2x - 8
Answer:
D) g(x) = 2x-8
Step-by-step explanation:
What are the solution points for the system graph?
A)
(0,2)
B)
No solution
C)
(0,1)
D)
(0,0)
Answer:
if i right it (0,2)
Step-by-step explanation:
i hope u get it right
Answer:
No Solutions
The two equations do not have any intersecting points, so the answer would be zero solutions.
Step-by-step explanation:
A pair of shoes is ticketed $49.99 but marked 15% off. You had a coupon for an additional 10% off the sales price. You have to pay 6.75% sales tax on shoes. How much are you paying?
Answer:
$40.86
Step-by-step explanation:
just multiply 49.99 times 0.15 then multiply 49.99 times 0.10 then add those together to get 12.49 then multiply 49.99 times 0.0675 to get 3.37 then subtract 12.49 from 49.99 then add 3.37 to that so like
(49.99 - 12.49) + 3.37 = 40.86
PLEASE HELP QUICKLY AS POSSIBLE THANK YOU :)
Answer:
12
Step-by-step explanation:
Answer: 12
Step-by-step explanation: Subtract 6 - 4 = 2. 2 * 2 = 4. 4 + 5 = 9. 9 - 3 = 6. 6 +6 = 12
Cherise plays basketball. The list shows the number of points she scored in each of her last six games. 12. 16. 10. 26, 14, 12 What is the mean number of points Cherise scored? O A 12 B. 13 C. 15 D. 16
anser:15
Step-by-step explanation:first add 12+16+10+26+14+12=90divide by how mnay numbers in this case 6 90 divied=15
Mean of given dataset is 15.
What is mean?It is the sum (total) of all the values in a set of data, such as numbers or measurements, divided by the number of values on the list is called mean.
Given dataset
12, 16, 10, 26, 14, 12
Mean = [tex]\frac{12+16+10+26+14+12}{6}[/tex]
= [tex]\frac{90}{6}[/tex]
= 15
Mean of given dataset is 15.
Find out more information about mean here
https://brainly.com/question/11163338
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The population of cina is approximately 1.381×10^9 and the population of the united states is approximately 3.23×10^8 about how many people live in both countries combined?Express your answer in scientific notation
Answer:
The number of people living in both countries is 1.704 x 10⁹
Step-by-step explanation:
Given;
Population of people in China, = 1.381 x 10⁹
Population of people in united states, = 3.23 x 10⁸
The total number of people living in both countries is given as;
Total population = 1.381 x 10⁹ + 3.23 x 10⁸
Total population = 1.381 x 10⁹ + 0.323 x 10⁹
Total population = (1.381 + 0.323) x 10⁹
Total population = 1.704 x 10⁹
Therefore, the number of people living in both countries is 1.704 x 10⁹
Juan is three times as old as Gabe and Gabe is six years older than Catherine. If the sum of their ages is 149, how old is each person? Define a variable, write an equation, solve the equation, and answer in a complete sentence. (Remember to clearly show your work on your work page.)
Answer:
Juan = 93 years.
Gabe = 31 years.
Catherine = 25 years.
Step-by-step explanation:
Let the age of Juan = J
Let the age of Gabe = G
Let the age of Catherine = C
Translating the word problem into an algebraic equation, we have;
[tex] J = 3G[/tex] ..........equation 1
[tex] G = C + 6 [/tex] ........equation 2
[tex] J + G + C = 149 [/tex] ........equation 3
We would solve the linear equations by using the substitution method;
Substituting equation 2 into equation 1;
[tex] J = 3(C + 6)[/tex]
[tex] J = 3C + 18[/tex] ........equation 4
Substituting equation 2 and equation 4 into equation 3;
[tex] (3C + 18) + (C + 6) + C = 149 [/tex]
Simplifying the equation, we have;
[tex] 5C + 24 = 149[/tex]
[tex] 5C = 149 - 24[/tex]
[tex] 5C = 125[/tex]
[tex] C = \frac {125}{5}[/tex]
C = 25 years.
To find G; from equation 2
[tex] G = C + 6[/tex]
Substituting the value of "C" into equation 2, we have;
[tex] G = 25 + 6[/tex]
G = 31 years.
To find J; from equation 1
[tex] J = 3G [/tex]
Substituting the value of "G" into equation 1, we have;
[tex] J = 3 * 31[/tex]
J = 93 years.
Therefore, Juan is 93 years old, Gabe is 31 years old and Catherine is 25 years old.
PLEASE HELP!!!
The ratios 12:24, 15:30, and 18:36 form a pattern of equivalent ratios in the multiplication table below.
A multiplication table.
Which method can find other equivalent ratios for this pattern?
Multiply 3 and 6 by the same factor, and write the products as a ratio.
Multiply 2 and 8 by the same factor, and write the products as a ratio.
Multiply 4 and 6 by the same factor, and write the products as a ratio.
Multiply 1 and 8 by the same factor, and write the products as a ratio.
Answer:
A
Step-by-step explanation:
Trust me on this.
Can I have brainlest, also I hope you do well!
Answer:
Multiply 3 and 6 by the same factor, and write the products as a ratio.
Step-by-step explanation:
because i have dun it
A bakery made 140 buns. A restaurant bought 80 of the buns. The remaining buns were put into bags of 4 buns each. How many bags of buns
are there?
Answer:
A bakery made 140 buns. A restaurant bought 80 of the buns. The remaining buns were put into bags of 4 buns each. How many bags of buns
are there?
Answer:
30, 30 bags of buns your welcome
Ann's gym charges $20 per month plus $5 per visit. Blake's gym charges
$30 per month plus $3 per visit. Ann and Blake make the same number of
visits per month. How many visits would make their monthly costs equal?
O A. At 5 visits they will both cost $45
B. At 8 visits they will both cost $60
C. They will never cost the same
0
D. They will always cost the same
Edit:
Answer:
yea i def lost brain cells trying to answer this
Step-by-step explanation:
Answer:
It's A!
Step-by-step explanation:
Basically, I substituted numbers in and added the per-month cost and per-visit cost:
Ann: 25 Blake: 33 (1 visit)
Ann: 30 Blake: 36 (2 visits)
Ann: 35 Blake: 39 (3 visits)
Ann: 40 Blake: 42 (4 visits)
Ann: 45 Blake: 45 (5 visits)
What is 4% of 25?.....
Answer:
1
Step-by-step explanation:
multiply 25 by .04
What is the Least Common Denominator for the two fractions? 1/4 and 7/10
Answer:
1/4
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
When are two lines parallel?
A. when the slopes are positive
B. when the slopes are equal
C. when the slopes are opposite
D. when the product of the slopes is –1
Answer:
B
Step-by-step explanation:
what is the greatest factor (GCF) of 66 and 22
Answe
22 is your answers ....
A train travels at a speed of 58.6 km/h. Express this speed in
a. m/s
b. cm/min
Answer:
16.27778 m/s
97666.6667 cm/min
Step-by-step explanation:
a. To convert km/hr into m/sec, multiply the number by 5 and then divide it by 18.
m/s = (58.6 * 5) /18 = 16.27778 m/s
b. 1 Kilometer/Hour = 1666.66666666667 Centimeter/Minute
so 58.6 * 1666.666 =97666.6667 cm/min
Help me and I’ll give brainliest to u
Answer:
7p
Step-by-step explanation:
Since it is 7 dollars per person, and p stands for person, the admission fee would be 7p.
Thank you, I hope you learned from this answer! If it did help, please mark this as brainliest! Thank you!
HELP WILL MARK BRAINLIEST
Answer:
i think d
Step-by-step explanation:
im so sorry if this is wrong but im almost positive its d
please mark brainliest
Last year, Deanna bought 225 lamps when customers needed 250 lamps. This year, she bought 300 lamps but only sold 200 lamps. Which set of statements about the percent errors for the two years is true?
Answer:
b.
Step-by-step explanation:
the percent error for this year was higher. deanna estimated better last year.
hope it helps!
I need help plz on this question
Answer:
-1/3
Step-by-step explanation:
Which statement best describes the graph
Answer: Its the first one
Step-by-step explanation:
I did it
x + y = 42, xy = 108 then what is x and y. Is there any (non-quadratic)formula for finding this instead of the process of elimination
Answer:
when x = 39.25, y = 2.75
when x = 2.75, x = 39.25
Step-by-step explanation:
use substitution method
x+y = 42 ------ (1)
xy = 108 ------ (2)
from (1) ,
x+y = 42
y = 42-x ------ (3)
substitute (3) into (2)
xy = 108
x( 42-x ) = 108
42x - x² = 108
-x² + 42x - 108 = 0
x² - 42x + 108 = 0
use the following formula to solve the value of x:
[tex]i) \: x = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \: \\ ii) \: x = \frac{ - b - \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
a = 1
b = -42
c = 108
[tex]i) \: x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
[tex]x = \frac{ - ( - 42) + \sqrt{( - 42) {}^{2} - 4(1)(108)} }{2(1)} [/tex]
[tex]x = \frac{42 + \sqrt{1764 - 432} }{2} [/tex]
[tex]x = \frac{42 + \sqrt{1332} }{2} [/tex]
[tex]x = \frac{42 + 6 \sqrt{37} }{2} [/tex]
[tex]x = 21 + 3 \sqrt{37} [/tex]
[tex]x = 39.25[/tex]
[tex]ii) \: x \: \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
[tex]x = \frac{ - ( - 42) - \sqrt{( - 42) {}^{2} - 4(1)(108} }{2(1)} [/tex]
[tex]x = \frac{42 - \sqrt{1764 - 432} }{2} [/tex]
[tex]x = \frac{42 - \sqrt{1332} }{2} [/tex]
[tex]x = \frac{42 - 6 \sqrt{37} }{2} [/tex]
[tex]x = 21 - 3 \sqrt{37} [/tex]
[tex]x = 2.75[/tex]
the 2 values of x are x = 39.25 and x = 2.75
substitute x = 39.25 into (3)
y = 42-x
y = 42-39.25
y = 2.75
substitute x = 2.75 into (3)
y = 42-x
y = 42-2.75
y = 39.25
when x = 39.25, y = 2.75
when x = 2.75, x = 39.25
HELP PLEASE!!!!
Review the function equation below.
y = −9x + 3
Enter the slope of the function in the box.
-9 is the answer
your welcome
Find all real values of x that satisfy the equation x^2 - 7x = 98.
The points (5, 7) and (4, 5) fall on a particular line. What is its equation in slope-intercept
form?
Answer:
y=2x−3
Step-by-step explanation:
What is the value of the x variable in the solution to the following system of equations? (1 point)
4x + 2y = 12
x − y = 3
0
−3
3
2
Answer:
-3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
4x + 2y = 12
x − y = 3
Make it able to cancel the variable y.
x*2 − y*2 = 3*2
2x − 2y = 6
Add the equations together now that y can be canceled out. Add each like term of the separate equations together.
4x + 2y = 12
+ 2x − 2y = 6
6x + 0 = 18
6x = 18
6 6
x = 3
I hope this helps!
What happens to the graph of f(x) when it is multiplied
by a number between - 1 and 0?