For each function below, identify and enter the percent rate of change per unit, t. Round to the nearest tenth of a percent.
Then use the drop-down menus to classify each as exponential growth or decay
Answers
The percentage rate of change of the given functions is given by the
derivative of their natural logarithm.
Responses:
[tex]f(t) = 1.18^t[/tex]
16.6%, exponential growth[tex]g(t) = 2^{-2 \cdot t}[/tex]
-138.6%, exponential decay[tex]h(t) = 1.19^{\frac{t}{10} }[/tex]
1.7%, exponential growth[tex]k(t) = 0.13^t[/tex]
-204%, exponential decayWhich method is used to determine the percentage rate of change?The percentage rate of change can be presented as follows;
[tex]Percentage \ rate \ of \ change = \mathbf{100 \times \dfrac{d}{dt} ln \left(f(t)\right)}[/tex]
[tex]f(t) = \mathbf{ 1.18^t} \ gives;[/tex]
[tex]100 \times \dfrac{d}{dt} \left( ln \left(1.18^t\right) \right) = \mathbf{ 100 \times ln(1.18)} \approx \underline{16.6\%}[/tex], exponential growth[tex]g(t) = \mathbf{2^{-2 \cdot t} }\ gives;[/tex]
[tex]100 \times \dfrac{d}{dt} \left( ln \left(2^{-2 \cdot t}\right) \right) = \mathbf{ 100 \times -2 \times ln(2)} \approx \underline{ -138.6 \%}[/tex] , exponential decay
[tex]h(t) = \mathbf{1.19^{\frac{t}{10} } }\ gives;[/tex]
[tex]100 \times \dfrac{d}{dt} \left( ln \left(1.19^{\frac{t}{10} }\right) \right) = \mathbf{ 100 \times \dfrac{10 \cdot ln(1.19)}{100}} \approx 1.7 \%[/tex], exponential growth
[tex]k(t) = \mathbf{ 0.13^t} \ gives;[/tex]
[tex]100 \times \dfrac{d}{dt} \left( ln \left(0.13^t }\right) \right) = \mathbf{100 \times ln(0.13)}\approx -204 \%[/tex], exponential decay
Learn more about exponential functions here:
https://brainly.com/question/14325265
Related Questions
Set 2 Maths has 30 pupils in it.
Set 1 Maths has 80% of the number of pupils in Set 2
How many pupils does Set 1 Maths have?
Answers
What is the domain of this relation?
(16, 1)
(0, 19)
(7, –19)
Answers
Answer:
{ 0 , 7 , 16 }
Step-by-step explanation:
Domain = set of x values
(16,1) x = 16
(0,19) x = 0
(7,-19) x = 7
The set of x values ( domain ) would be
{ 0 , 7 , 16 }
Note: the values of the domain should be put in order from least to greatest
What is the answer to this question
Answers
Answer:
B - Congruent : SAS
Step-by-step explanation:
We are given that there are two sides that are congruent and one angle is congruent and it is in the order Side Angle Side.
Help me with this problem
Answers
Answer:
Angle A is F Angle A = 57. 52+71=123. 180-123=57
identify the unit rate shown in the graph
Choices:
A. 1/3 mile per hour
B. 3 hours per mile
C. 3 miles per hour
D. 4 miles per hour
Answers
The answer is C or 3 miles per hour
how is it 3?:
there is a point at 6 and another at 3 all we do is 6 - 3 = 3
A circular garden is surrounded by a circular path of 7m width.If the area of path is 770m²,find the area of the garden without path.
help me this question ⁉️
Answers
Answer:
Answer:
Radius of the circular garden
= 210 sq
=105m
Radius of the region covering the garden and the path =105m+7m
=112m
Area of the region between two concentric circles
with radius of outer circle R, and inner circle r =π(R sq−r sq)
Hence, the area of the path
=π(112sq−105 sq)= 7/22
(12544−11025)
= 33418/7
=4774m sq
HOPE THIS WILL HELP YOU MATE
Brainly to whomever somehow solves for g & k. I WILL REPORT SCAMS AND UNHELPFUL/ UNRELATED ANSWERS.
Answers
Answer:
g = 48
k = 18
Step-by-step explanation:
h / 10 = 60 / 12
h / 10 = 5
h = 5 x 10
h = 50
40 / h = g / 60
40 / 50 = g / 60
4 / 5 = g / 60
g = ( 60 x 4 ) / 5
= 12 x 4
g = 48
90 / k = 60 / 12
90 / k = 5
k = 90 / 5
k = 18
HELP HELP HELPPPP PLEASEEE
Directions: Determine if segments AB and CD are parallel, perpendicular, or neither.
AB formed by (-2, 13) and (0, 3)
CD formed by (-5, 0) and (10, 3)
Answers
Given:
AB formed by (-2,13) and (0,3).
CD formed by (-5,0) and (10,3).
To find:
Whether the segments AB and CD are parallel, perpendicular, or neither.
Solution:
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
AB formed by (-2,13) and (0,3). So, the slope of AB is:
[tex]m_1=\dfrac{3-13}{0-(-2)}[/tex]
[tex]m_1=\dfrac{-10}{2}[/tex]
[tex]m_1=-5[/tex]
CD formed by (-5,0) and (10,3). So, slope of CD is:
[tex]m_2=\dfrac{3-0}{10-(-5)}[/tex]
[tex]m_2=\dfrac{3}{10+5}[/tex]
[tex]m_2=\dfrac{3}{15}[/tex]
[tex]m_2=\dfrac{1}{5}[/tex]
Since [tex]m_1\neq m_2[/tex], therefore the segments AB and CD are not parallel.
[tex]m_1\times m_2=-5\times \dfrac{1}{5}[/tex]
[tex]m_1\times m_2=-1[/tex]
Since [tex]m_1\times m_2=-1[/tex], therefore the segments AB and CD are perpendicular because product of slopes of two perpendicular lines is always -1.
Hence, the segments AB and CD are perpendicular.
Answer:
AB is perpendicular to CD.
Step-by-step explanation:
AB formed by (-2, 13) and (0, 3)
CD formed by (-5, 0) and (10, 3)
Slope of a line passing through two points is
[tex]m= \frac{y''-y'}{x''- x'}[/tex]
The slope of line AB is
[tex]m= \frac{3- 13}{0+2} = -5[/tex]
The slope of line CD is
[tex]m'= \frac{3 -0 }{10+5} = \frac{1}{5}[/tex]
As the product of m and m' is -1 so the lines AB and CD are perpendicular to each other.
What is the value of the expression below
(-64)^2/3
Answers
Answer:
16
Step-by-step explanation:
[tex](-64)^2/3[/tex]
64 = [tex]2^{6}[/tex]
[tex]2^{6} ^{\frac{1}{3} } ^{2}[/tex]
[tex]2^{ 2^{2} }[/tex]
[tex]2^{4}[/tex]
16
This pattern follows the rule add 14. What other features do you observe?
13, 27, 41, 55
All terms are even because even + even = even.
All terms are even because odd + odd = even.
All terms are odd because odd + even = odd.
All terms are even because when you add two numbers together, the sums are always even.
Answers
Solve the inequality -10w _< 20
Answers
Step-by-step explanation:
-10w< 20w< 20/-10w< -2hope it helps
stay safe healthy and happy...In the history of Major League Baseball, the most valuable player award has been won by players from 7 different countries. which countries were they
Answers
Answer:
United States, Canada, Dominican Republic, Cuba, Venezuela, Japan, Panama
Step-by-step explanation:
Taking a look at a list of Major League Baseball most valuable players, the countries are:
United States(most players are US-born).
Canada(Joey Votto in 2010).
Dominican Republic(Albert Pujols and Vlad Guerrero Sr. for example).
Cuba(last Jose Abreu in 2020)
Venezuela(last Jose Altuve in 2017)
Japan(Ichiro in 2001).
Panama(Rod Carew)
Question 5 can I have as much as you can do please
Answers
Answer:
x = 12
Step-by-step explanation:
The sum of angles in a triangle is 180°
Thus,
(x + 20) + (10x) + (x + 16) = 180°
Collect like terms
x + 10x + x + 20 + 16 = 180°
12x + 36 = 180°
12x = 180 - 36
12x = 144
Divide both sides by 12
x = 144 ÷ 12
x = 12
Substitute the value of x into the question
Therefore,
x + 20 = 12 + 20
= 32°
10x = 10(12)
= 120°
x + 16 = 12 + 16
= 28°
In general, a gallon of paint can cover 400 square feet. Muhanmmad needs to cover a 21 foot by 17 foot wall and a circular area with a 5 foot radius. How many gallons will he have to buy?
Answers
Answer:
1.1 gallons of paint
Step-by-step explanation:
The wall measures;
21 foot by 17 foot
Thus, area of wall = 21 × 17 = 357 ft²
Circular area has a radius of 5 ft.
Thus;
Area of circle = πr² = π × 5² = 78.54 ft²
Total area covered = 357 + 78.54 = 435.54 ft² ≈ 436 ft²
A gallon of paint can cover 400 ft²
Thus gallons Muhammad would need = 436/400 = 1.09 gallons ≈ 1.1 gallons
Question 4 (True/False Worth 4 points)
(0701)
True or False?
is a solution to the inequality 12+2 < 12
True
O False
Answers
Explanation:
Because the 12+2 on the left side isn’t less than twelve. This makes it false.
Mr. Tanaka is making Miso soup for his family. The recipe calls for 350 ml of Dashi. Mr. Tanaka plans to make a smaller batch using 280 ml of dashi. He wants to know what percent of the stock he will use compared to the original recipe. PLSS HELPPPPPPP Quick
Answers
please help!!!
Simplify
3+ 7 X 4
Answers
Answer:
31
Step-by-step explanation:
[tex]3+7[/tex] × 4 Multiply first
3 + 28 Then add
31
Step 1: Rewrite equation
To start off, I find it helpful to rewrite the equation, in order to better understand the problem we will be solving.
3+7×4
Step 2: Solve using PEMDAS
To solve the equation, we will be using PEMDAS. Remember that we must solve in the correct sequence. In order of operations, p stands for parentheses, e stands for exponents, m stands for multiplication, d stands for division, a stands for addition, and s stands for subtraction. The only two shown in this equation are multiplication and addition. As per the order in PEMDAS, let’s multiply first and then add.
3+7×4
3+28
31
31 is your answer. Hope this helps! Comment below for more questions.
17:56 Dawn is trying to find out how much weight she can push across the room. She is really trying to find her __________.
Answers
If an item weighs 45kilograms what is its weight in pounds
Answers
is the weight.
Expand the following using the Binomial Theorem and Pascal’s triangle (2x − 3y)^4
Answers
Answer:
Step-by-step explanation:
Binomial Expansion:
[tex](2x-3y)^4 \\\\= 4C_0(2x)^4 (-3y)^0 + 4C_1(2x)^3 (-3y)^1 + 4C_2(2x)^2(-3y)^2 \\\\+ 4C_3(2x)^1 (-3y)^3 + 4C_4(2x)^0 (-3y)^4\\\\=16x^4 + 4(8x^3)(-3y) + 6(4x^2)(9y^2) + 4(2x)(-27y^3) + 81y^4\\\\=16x^4 - 96x^3y + 216x^2y^2-216xy^3 +81y^4[/tex]
Pascal's Triangle:
Zero row 1
First row 1 1
Second row 1 2 1
Third row 1 3 3 1
Fourth row 1 4 6 4 1
What is the value of x?
0 14
0 17
O 27
O 34
PLEASE HELP
Answers
What is the value of X?
3
4
6
8
Answers
Answer:
The answer is 4
Step-by-step explanation:
product of -2/3 and 5 2/4?
Answers
Answer: [tex]-\frac{11}{3}[/tex]
Step-by-step explanation:
[tex]-\frac{2}{3} *5\frac{2}{4} \\\\\\=-\frac{2}{3} *5\frac{1}{2} (5\frac{1}{2} =\frac{5*2}{2} +\frac{1}{2} =\frac{10+1}{2} =\frac{11}{2})\\\\\\=-\frac{2}{3} *\frac{11}{2} =-\frac{11}{3}[/tex]
Which integers could you add to −18 to get a sum that is greater than 5?
Answers
Answer:
23
Step-by-step explanation:
-18+(18+5) = 5,
so adding any integer that is greater than (18+5)=23 will give a sum that is greater than 5.
Answered by GAUTHMATH
Find each measure
Please help me
Answers
Answer:
19) 100
20) 360 - 90 = 270
21) 360- 125 = 235
22) 45
Step-by-step explanation:
Central angles and the arcs they create are congruent.
What percent did the price drop
Answers
Answer:
10%
Step-by-step explanation:
You have the correct answer. Nice job!
A client has two refrigerators, one in the kitchen and one in the basement.The former is new and efficient. The latter is 30 years old and uses 120Kwh/month. If this client pays 0.15/kwh
Answers
Incomplete question: we assume figures to explain further
Answer and explanation:
Given that client pays $0.15/kwh
If old fridge is inefficient and consumes 120kwh/month
And new fridge is efficient and therefore consumes 50kwh/month
For the old fridge, client will be paying
120×0.15= $18 per month on electricity charges
For the new fridge, client will be paying
50×0.15= $7.5 per month on electricity charges
Find the HCF of
[tex] 4x {}^{2} y \: and \: 12xy {}^{3} [/tex]
Answers
Answer:
I hope the pic i gave is helpful!!!
find the area of the rectangle whose dimensions are 9cm and 8cm.
Answers
Answer:
72 cm²
Step-by-step explanation:
Area = 9(8) = 72
..............
A certain ferry moves up and down a river between Town A and
B. It takes the ferry two hours to travel to Town A and only an
hour and thirty minutes to return to Town B. If the current is 5mph
how far apart are the two cities?
Answers
Answer: 60 miles
Step-by-step explanation:
Given
It takes ferry 2 hours to travel to town A and only [tex]1.5\ hr[/tex] to travel back to town B.
Speed of current is [tex]u=5\ mph[/tex]
Suppose the speed of the ferry is [tex]v[/tex] mph
Distance traveled in both the cases is same, but it took more time traveling to city A that is, ferry is moving upstream and downstream for returning time.
[tex]\Rightarrow 2(v-5)=1.5(v+5)\\\Rightarrow 2v-10=1.5v+7.5\\\Rightarrow 0.5v=17.5\\\Rightarrow v=35\ mph[/tex]
Distance between the towns is [tex]2\times (35-5)=60\ \text{miles}[/tex]
Answer:
The distance between the two towns is 60 miles.
Step-by-step explanation:
Let the distance between A and B is d.
A to B , t = 2 hour
B to A , t' = 1.5 hour
Speed of current, u = 5 mph
Let the speed of ferry is v.
distance = speed x time
d = (v - 5) x 2 = (v + 5) x 1.5
2 v - 10 = 1.5 v + 7.5
0.5 v = 17.5
v = 35 mph
So, the distance is
d = (35 - 5) x 2 = 60 miles.
