Answer:
Step-by-step explanation:
Let P be the number of phone cases and C the number of chargers.
p($25) + C($30) ≤ $100
and
P + C ≥ 4
The population of a pigeons in a city is 100 and is growing exponentially at 20% per year. Write a function to represent the population of pigeons after
t
t years, where the monthly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per month, to the nearest hundredth of a percent
Answer:
p(t) = 100×1.0153^(12t)1.53% per monthStep-by-step explanation:
In general, the function will be written ...
p(t) = (initial value)×(growth factor)^t
where t is in units comparable to those applicable to the growth factor. The growth factor is found from ...
growth factor = 1 + growth rate
Here, the growth rate is given as 20% per year, so the growth factor per year is ...
1 +20% = 1.20
The initial value is given as 100, so we can write the exponential function as ...
p(t) = 100×1.20^t
__
The time period units for t are supposed to be years, but we want to find the growth rate for a month. We can do that by recognizing there are 12 months in a year. In the above equation, we can use (1/12)(12t) in place of t, then figure the growth factor (and growth rate) per month.
p(t) = 100×(1.20^(1/12))^( 12t)
p(t) = 100×1.0153^(12t) . . . . population exponential function
This shows the monthly growth factor is 1.0153, so the monthly rate of change (growth rate) is ...
1.0153 -1 = 0.0153 = 1.53% . . . . monthly rate of change
Answers:
Function is [tex]P(t) = 100(1.0153)^{12t}\\\\[/tex]Monthly growth rate is roughly 1.53%=====================================================
Explanation:
The population starts at 100 pigeons. After a year, the population goes up by 20%, meaning the population goes up by 20. It lands on 120 after a full year (100+20 = 120).
Dividing the "before" and "after" population amounts gets us 120/100 = 1.20
If we didn't worry about the monthly rate, and only cared about the annual rate of growth, then the population function would be
[tex]P(t) = 100(1.20)^t[/tex]
where t is the number of years and P(t) is the population for that year number. Notice how the 1.20 is the base of the exponential to quickly tell the reader the annual rate of growth. We read off the .20 portion and that converts to 20% after moving the decimal 2 spots to the right.
If we were to plug t = 0 into that function, then we'd get P(0) = 100. Inputting t = 1 leads to P(1) = 120. This helps confirm we have the correct annual growth rate function.
---------------------
Unfortunately, your teacher doesn't want the annual growth rate function. Instead, they want you to write a function where the reader can easily pick out the monthly rate of change without having to do any math. This is due to the instructions that "the monthly rate of change can be found from a constant in the function". Let m be this constant.
Since t is the number of years, this means t = 1/12 represents 1/12 of a year, aka 1 month. If you were to compute P(1/12), then you should get roughly 101.530947049973
Divide this amount over the initial population to find m.
m = 101.530947049973/100 = 1.01530947049973
So we get m = 1.0153 after rounding to four decimal places.
The number m is in the form 1+x. Solving 1+x = m will lead to x = 0.0153 to indicate a monthly rate of change is roughly 1.53% since we move the decimal point 2 spots to the right to go from 0.0153 to 1.53%
The pigeon population is increasing by roughly 1.53% each month.
This is why computing this m value leads to the reader able to spot the monthly rate of change without having to resort to a calculator. All they have to do is read the digits to the right of the decimal point and convert that to percentage form.
---------------------
An alternative way to compute this value is to use this formula
m = (1+r)^(1/12)
We'll plug in the annual rate r = 0.20 to get:
m = (1+r)^(1/12)
m = (1+0.20)^(1/12)
m = 1.01530947049973
m = 1.0153
We get the same approximate value as earlier.
---------------------
Whichever method you use, you should get roughly m = 1.0153
We're given that A = 100 is the initial population
So we'll then be able to form this function
[tex]P(t) = A*(m)^{12t}\\\\P(t) = 100(1.0153)^{12t}\\\\[/tex]
This represents the monthly growth of the population where t is in years. Note that after something like t = 3 years, we have 12t = 12*3 = 36 months pass by. So that's why the 12t is in the exponent rather than simply t.
Once again, for comparison we have...
[tex]P(t) = 100(1.20)^{t}\\\\[/tex] for annual growth[tex]P(t) = 100(1.0153)^{12t}\\\\[/tex] for monthly growthEach function has t represent the number of years. The difference is the base of each exponential to tell us the respective annual or monthly growth rate. Also, the exponent up top must be adjusted depending on which you go for.
---------------------
You may be wondering: "what if the exponent in the monthly growth rate function wasn't 12t?". Let's find out. We'll assume the monthly growth rate function is [tex]P(t) = 100(1.0153)^{t}\\\\[/tex] and show that an error happens.
If we plugged in something like t = 1, we should get P(t) = 120 like mentioned earlier.
[tex]P(t) = 100(1.0153)^{t}\\\\P(1) = 100(1.0153)^{1}\\\\P(1) = 100(1.0153)\\\\P(1) = 101.53\\\\[/tex]
That value of 101.53 is the approximate population number after 1 month, rather than 1 year. Making the exponent 12t will fix the issue.
Which system of equations is equivalent to the following system? (5 points) 2x + 4y = 14 4x + y = 20
a.2x + 4y = 14
−16x − 4y = −80
b.2x + 4y = 14
−4x + y = −20
c.4x + 8y = −28
4x + y = 20
d.−2x − 4y = 14
4x + y = 20
Answer:
a.
Step-by-step explanation:
4x+y=20 multiplied by (-4) gives you -16x-4y=-80
The table shows the linear relationship between the number of pages left to read in an
the number of hours a student has already spent reading the novel. Mark each stateme
or false. If false, rewrite the statement correctly.
HOURS
READ
RE
9. The student reads at a rate of 48 pages per hour.
1
4
10. The number of pages in the novel is 644.
8
12
11. The situation can be represented by the
equation y = -48x + 692.
14
The table is an illustration of a linear function
9. The student's rate
Take any two points from the table
[tex](x,y) =\{(1,644)\ (4,500)\}[/tex]
The rate is then calculated using:
[tex]Rate = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
This gives
[tex]Rate = \frac{644 -500}{1-4}[/tex]
[tex]Rate = \frac{144}{-3}[/tex]
[tex]Rate = -48[/tex]
The statement that the student reads at a rate of 48 pages per hour is true
10. The pages in the novel
From the table, there are 644 pages left, after the student read for 1 hour.
This means that there are more than 644 pages in the novel.
The statement that the number of pages in the novel is 644 is false
11. The linear equation
This is calculated as:
[tex]y = Rate(x -x_1) + y_1[/tex]
So, we have:
[tex]y = -48(x -1) + 644[/tex]
[tex]y = -48x +48 + 644[/tex]
[tex]y = -48x +692[/tex]
The statement that the situation can be represented by the equation y = -48x + 692 is true
Read more about linear equations at:
https://brainly.com/question/15602982
Answer:
Step-by-step explanation:
ABC is a triangle. AC=19cm, BC=17cm and angle BAC=60
Answer:
In the picture
Step-by-step explanation:
it's an acute triangle
more information in the picture
Tyra, Elle, Tran, and Ann share equally in the rental of a car. If the total cost of the rental is C dollars, which expression represents Tyra's share of the cost?
Answer:
c/4
Step-by-step explanation:
Since it's equally shared, and the total cost is C, then the answer is c/4
find the ratio of : 800 ml to 4.8 litres
Answer:
The ratio is [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
We have
[tex]\frac{800mL}{4.8L} \\\\\frac{0.8L}{4.8L}\\\\\frac{1}{6}[/tex]
PLEASE NO LINKS AND NO NEGATIVITY
Answer:
Answer is 15-r .Hope it will help you
help me please asap
i will make you brainliest
Answer:
see explanation
Step-by-step explanation:
An open circle indicates that x cannot equal that value
A closed circle indicates that x can equal that value.
(i)
An open circle at x = - 1 and arrow pointing right
x > - 1
(ii)
An open circle at x = - 1.5 and arrow pointing right
x > - 1.5
(iii)
A closed circle at x = 4 and arrow pointing left
x ≤ 4
(iv)
A closed circle at 0.5 and arrow pointing left
x ≤ 0.5
The cost of an Uber is $8.00 plus $1.25 per
mile. Write a function, f(x), to determine the cost of an x-mile Uber ride.
Answer:
Cost = 8 + 1.25x
Step-by-step explanation:
What persent of 240.00 is 60?
Answer:
(240 × 60)/100 = 144
Step-by-step explanation:
(Whole × Percent)/100 = Part
Answer:
25%
Step-by-step explanation:
60 times 4 is equal to 240.
1/4 is 25%
60 is 25% of 240
What is the unit of time (t) when calculating interest?
Answer:
t = time in decimal years; e.g., 6 months is calculated as 0.5 years. Divide your partial year number of months by 12 to get the decimal years.
Step-by-step explanation:
pls help me with this:((((
Answer:
it's A (the first answer)
the second one is also A the height of the plant.
it's completely dependent on the starting size and the number of days.
what is the slope of the line 3x-4y=73x4y=7?
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
y = mx + b , "m" is slope and "b" is y-intercept
~~~~~~~~~~~~~
3x - 4y = 7
- 4y = - 3x + 7
y = [tex]\frac{3}{4}[/tex] x - [tex]\frac{7}{4}[/tex] ⇒ m = [tex]\frac{3}{4}[/tex]
I'm spending my last 10 points on this please help me
Answer:
Rate of sales tax = 6% of $60
Sales tax = [tex]\frac{6}{100}[/tex] × 60
= $3.60
1000000x900=?????????????
Answer:
The answer is 900000000
Answer:
900000000, or 9.0x 10^8
Step-by-step explanation:
do 1(9)=9
then add the 0's behind.
The cost of a season train ticket is reduced by $87.36 which corresponds to a 39% reduction. Find the original cost of the season ticket.
A new DVD player has a purchase price of $430. With the extended warranty, the total cost is $512. What percent of the purchase price is the price of the warranty? a. 16% b. 19% c. 24% d. 29% Please select the best answer from the choices provided A B C D.
The percent of the purchase price that is the price of the warranty is: b. 19%.
Using this formula
Purchase price percent=Total cost-Purchase price/Purchase price
Where:
Total cost=$512
Purchase price=$430
Let plug in the formula
Purchase price percent=$512-$430/$430
Purchase price percent=$82/$430
Purchase price percent=0.19×100
Purchase price percent=19%
Inconclusion the percent of the purchase price that is the price of the warranty is: b. 19%.
Learn more about purchase price here:https://brainly.com/question/6076645
How do I graph 2x-3?
A straight line passes through points (-1, 5) and (2, -4). What is the law of the function represented by this line?
Answer:
y = -3x+2
Step-by-step explanation:
See attachment.
Find the slope:
Rise = (-4 - 5) = -9
Run = (2 - (-1)) = 3
Slope(Rise/Run) = -3
Find the y-intercept:
y = mx + b
y = -3x + b
5 = -3*(-1)+b [Use point (-1,5)
b = 2
====
y = -3x + 2
GIVING BRAINLIEST
What is the solution to the system of linear equations graphed below?
Answer:
The first option so [tex](3\frac{1}{2}, -4)[/tex] is the answer
Skills required: Graphing Knowledge, Systems Knowledge
Step-by-step explanation:
1) The solution to any system is the intersection between any 2 lines or functions. In this case, we are given two functions on a graph, and need to find the solution to them. That is the intersection.
2) We can see the intersection and see that the x-axis value for the coordinate point is around 3 1/2 (or 3.5 -- whatever you prefer), and that the y-axis value for the point is -4.
Therefore, the coordinate point is: [tex](3\frac{1}{2}, -4)[/tex] since this answer best matches the coordinate values of that point.
==================================================================
Select the first option, have a nice day! :D
CAN SOMEONE HELP ME PLEASE ASAP!?
Answer:
7/20
Step-by-step explanation:
7 / 20 0.35
Answer:
7/20
100/20=5
7*5=35.
PLEASEEE HURRY
Please please please
Answer:
final answer is: ABC, A (-5,1), B (-4,6) and C (-1,4)
Step-by-step explanation:
Original: ABC, A (2,-1), B (1,4) and C (-2,2)
translate 3 units to the right and 2 units up: ABC, A (5,1), B (4,6) and C (1,4)
reflected over the x-axis: ABC, A (5,-1), B (4,-6) and C (1,-4)
rotated 180°: ABC, A (-5,1), B (-4,6) and C (-1,4)
The measure of an angle is 138°. What is the measure of its supplementary angle?
Answer:
Supplementary angle = 42⁰
Step-by-step explanation:
We know that
Sum of two supplementary angle = 180
Let,
Supplementary angle = x
=> 138 + x = 180
=> x = 180 - 138
=> x = 42⁰
If the measure of an angle is 138°, the measure of its supplementary angle is 42°
What are supplementary angles:Supplementary angles are two angles that sum to 180 degrees. The sum of supplementary angles is equals to 180 degrees.
Therefore, if the angles are x and y , For them to be supplementary,
x + y = 180°
If the measure is 138 degrees, the measure of its supplementary angle can be calculated as follows:
let
its supplementary angle = x
138 + x = 180
x = 180 - 138
x = 42°
learn more on supplementary angles: https://brainly.com/question/25818150?referrer=searchResults
Can you please help me with this question
Answer:
y = 1/2x-3
Step-by-step explanation:
y=mx+b, where m is slope and b is y-int and x and y are variables.
y = 1/2x-3
Plot your point at (8,1) and then use your slope and rise 1 go over 2 then draw your line.
Hope that helps
You must include an explanation accompanied with your solution. Answers without
explanations will not receive full credit: *
2 points
Mark invested $125. He earned a simple interest of 3% per year on the initial
investment. If no money was added or removed from the investment, what was
the amount of interest Mark received at the end of two years?
A. $5.70
B. $7.50
C. $75.00
D. $750.00
Your answer
Answer:
B) $7.50
Step-by-step explanation:
Interest (I) = Principal (P) x Interest Rate (r) x Time (t, in years)
I = 125(.03)(2)
I = 7.5
CAN SOMEONE HELP ME PLEASE ASAP!?
9. Determine whether the parallelogram is a rectangle, square, or rhombus. G(-4,3), D(2,1) F(-5, 0) and E(1, -2)
Answer:
rectangle
Step-by-step explanation:
Answer:
Rectangle
Step-by-step explanation:
FG's slope is the opposite reciprocal of GD's, so they are perpendicular. The same with the other sides.
The opposite sides have the same length.
Subtract: x2 + 2x + 1 – (x – 3)
Therefore, the answer is 3x - 2.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
please help NEED NOW
thank youu
Answer:
C
Step-by-step explanation:
not a hundred percent but it makes the most sense
mathematic equation
solve q
11=8(3q-1)
Step-by-step explanation:
11 = 8(3q - 1)
11 = 24q - 8
11 + 8 = 24q
19 = 24q
19/24 = q
q = 0.791666666666666
q = 0.8 to 1 decimal place