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
Jerry needs 216 posts to build a fence. He has 88 posts and needs P more. Write an equation that you could use to find the number of posts jerry still needs.
Answers
Answer:
P = 128 Post
Step-by-step explanation:
Total post needed = 216 posts
Number of post Jerry has = 88 posts
Number of posts jerry still needs = P
Total = Number of post Jerry has + Number of posts jerry still needs
216 = 88 + P
216 - 88 = P
128 = P
P = 128 Post
quall o numero de diagonais de um poligono com 15 lados
Answers
Answer:
90 diagonais.
Step-by-step explanation:
[tex]n(n-3)/2=15(15-3)/2=15*6=90[/tex]
How many odd numbers greater than 60000 can be formed, using numbers 2,3,4,5 and 6 if each digit is used only once in each number?
Answers
Hello,
All the numbers must begin with 6.
There are still 2,3,4,5 digits : 4 possibilities.
4!=4*3*2*1=24
The first is 62345 and the last 65432.
solve the system of equations using the substitution method pls show work
4x+y=7
3x+2y=9
Answers
Answer:
x = 1 ; y = 3Step-by-step explanation:
[tex]4x + y = 7 \\ y = 7 - 4x[/tex]
Now we know the value of y is 7 - 4x we plug this value to the second equation with y, So,
[tex]3x + 2(7 - 4x) = 9 \\ 3x + (14 - 8x) = 9 \\ - 5x = 9 - 14 \\ - 5x = - 5 \\ x = \frac{ - 5}{ - 5} \\ x = 1[/tex]
Now to find the value of y we use the first equation
[tex]y = 7 - 4x \\ y = 7 - 4(1) \\ y = 7 - 4 \\ y = 3[/tex]
Hope this helps you :)
Answer:
x = 6/5 or 1.2 y = 11/5 or 2.2
Step-by-step explanation:
4x + y = 7
y = -4x + 7
y = 7 - 4x
3x + 2y = 9
3x + 2(7 - 4x) = 9
3x + 14 - 8x = 9
-5× + 15 = 9
-5x = 9 - 15
-5x = -6
x = -6/-5
x = 6/5
4x + y = 7
4(6/5) + y = 7
24/5 + y = 7
y = 7 - 24/5
y = 35/5 - 24/5
y = 11/5
Given the following geometric sequence, Find the common ratio (3, 18,108)
Answers
Answer:
6
Step-by-step explanation:
3*6=18
18*6=108
There is $1.90 in a jar filled with
quarters, dimes, and nickels.
There are 2 more quarters than
dimes and there are 2 more
nickels than quarters.
How many of each coin are there?
Answers
Answer:
7 nickels, 5 quarters, 3 dimes
Step-by-step explanation:
7 nickels= 35 cents
5 quarters= $1.25
3 dimes= 30 cents
35+ 1.25+ 30= $1.90
Hope this helps!
Plz mark Brainliest if u can :)
Can someone please help?
Answers
Answer:
f(x) = (x + 4)^2 - 5
Step-by-step explanation:
Parent function: f(x) = x^2
To show this in a way that may look more familiar, f(x) = 1(x - 0)^2 + 0
Vertex form: f(x) = a(x - h)^2 + k
We know a = 1, because the slope is the same as the parent function.
Vertex: (h,k)
We can see that the vertex of the graph is (-4, -5)
So h = -4 and k = -5
Now all we need to do is plug the variables into our equation.
f(x) = a(x - h)^2 + k
f(x) = 1(x + 4)^2 - 5
f(x) = (x + 4)^2 - 5
4 + {−5 + [−3 + 4 + 2(−7 + 4) + 4] + 2}
7 + {−2 + [5 + 4(−3) + (−6 + 2) + (−3)]}
(−2) + {3 + [−4 + (3)] + 7} + (−5)
(−10) + {−7 + [−4 + 5(−9) + 5] + 8}
18 + 3{−4 + [−15 + 20 + (−3)] + (−9)}
−(−8 + 5) + {−4 + [−7 + (−9 − 5) + 3]}
− 9 + {−7 − 2[−(4 + 1) + (5 − 9)]} − 3
−1 − 3{6 − [4 + 2(−7 + 8) − 5] − 2}
−(−2) − {−(−7) + [−3 + (−5 − 2) + 6]}
−(−6 − 2) − 2{−4(−5) + 5[−3 + (−2)]}
6 − 2{−4 + 3[3 − 3(−8 − 5) + 14] − 7}
Me pueden ayudar por favor es urgente!!! y Buenas Noches ;)
Answers
Answer
it is 5 : )
Step-by-step explanation:
Use two unit multipliers to convert 36 inches to miles.
Answers
Answer:
36 inches = 0.000568182 miles
I need who help .. who can be my lifesaver
Answers
Answer:
Q = G
Step-by-step explanation:
We are already given that angle P = angle H
We are also given that side QP = side GH
Remember if two sides are congruent then so are their opposite angles meaning that the opposite angle of GH ( which would be angle F ) would be congruent to the opposite angle of QP ( which would be angle R )
The remaining angles would be angle q and angle g so the additional information needed would be G = Q
The proportion of observations from a Standard Normal Distribution that take values larger than -0.8 is about:
Answers
Answer:
0.78814
Step-by-step explanation:
From. The Z probability distribution table ;
The values larger than - 0.8
P(Z ≤ - 0.8) = 0.21186
P(Z > - 0.8) = 1 - P(Z ≤ - 0.8)
1 - P(Z ≤ - 0.8) = 1 - 0.21186
P(Z > - 0.8) = 1 - 0.21186 = 0.78814
Which of the following quadratic regression equations best fits the data
shown below?
Х
-4
-3
-2
-1
0
1
N
3
4
y
35
20
10
5
00
10
15
30
48
O A. y = 0.98x2 +3.06x+ 6.02
O B. y = 2.23x2 + 1.62x+ 5.26
O c. y = 3.72x2 + 2.94x + 3.21
O D. y = 4.63x2 + 0.84x+ 4.14
Answers
Answer:
C
Step-by-step explanation:
The method that is not used on graphs to lead the reader to misinterpret the graph is - Comparing two sets of related data on the same graph for the sake of comparison.
What is graph?A graph is a intersection of {x} and {y} axis. On the graph, the coordinate points can be plotted in the form (x, y). In this, {x} represents the horizontal distance along the {x} axis and {y} is the vertical distance along the {y} axis.
Given is to identify the methods that are not used on graphs to lead the reader to misinterpret the graph.
The method that is not used on graphs to lead the reader to misinterpret the graph is - Comparing two sets of related data on the same graph for the sake of comparison.
Therefore, the method that is not used on graphs to lead the reader to misinterpret the graph is - Comparing two sets of related data on the same graph for the sake of comparison.
To solve more questions on graphs, visit the link below-
https://brainly.com/question/17267403
#SPJ7
How many digits from 10 to 1000 have each digit greater than its following digit?
Answers
Answer:
10 has 2 digits
1000 has 4 digits
Difference of 2 digits
The Banker's Rule is another type of simple interest computation that is similar to ordinary simple interest computation. It is based on a 360-day year, but you use the actual number of days in the term when calculating interest. Does this benefit the lender or the borrower? Explain.
Answers
Answer:
it would appear tp benefit the borrower. if interest (which is paid by the borrower) is computed on a 360 day year and there are 365 days in a year....
one could consider the "Bankers Rule" to give the borrower 5 "free" days of no interest paid
Step-by-step explanation:
Find y
Help me please
Answers
Answer:
y = 46
Step-by-step explanation:
Stacy is building a candy house. She
worked on it 3 hours before lunch and
6 hours after lunch. How many total
hours did Stacy spend working on the
candy house?
Answers
Answer:
9 hours
Step-by-step explanation:
You have to add both hours to get the total amount. So 3+6=9
Answer:
9 hours
Step-by-step explanation:
Stacy worked on the house 9 hours because she worked 3 hours before lunch and 6 hours after lunch. 6+3=9
Which of the following statements is true for the figures shown
Answers
Answer:
no question pls give and I can think
Lines A and B are parallel
NEED HELP, IF ITS RIGHT ILL MAKE YOU BRAINLIEST
Answers
130 is your answer! Look at line A. 130 degrees. now if A and B are parallel then 5 on line B will also be 130 degrees.
I hope this helps!
£410 is divided between Gordon, Malachy & Paul so that Gordon gets twice as much as Malachy, and Malachy gets three times as much as Paul. How much does Malachy get?
Answers
Answer:
malachy got 123 euros
Step-by-step explanation:
if i m right than give me brainliest
3 Nine children share out cqually the chocolates in a large tin and it
cight cach. If there were only six children, how many would each get
Answers
A larger number is double the sum of 3 and a smaller number. The larger number is 2 less than 3 times the smaller
number. If y represents the larger number and x represents the smaller number, which equations model the situation?
Check all that apply.
Oy - 3x-2
3x-y = 2
3x-y=-2
y=2-3x
Oy=2(x+3)
Answers
Answer:
not sure what the O is there for?
if it is zero then Oy would make Oy=2(x+3) not correct
3x-y = 2
y=2(x+3)
Step-by-step explanation:
)
question is on the image.
can you do question a and b please
I'll you give the brainliest.
Answers
Answer:
a) i. 1/6
ii. 0
b) 1/6 * 60
=10
Answer:
[tex]a) 1)\frac{1}{6} \\ \\ 2)0 \\ \\b) \frac{1}{6} \times 60 = \frac{60}{6} = 10[/tex]
hope this helps you.
simplyfy using appropiate properties 1/4×2/5+-1/6×3/2+3/7×2/5
Answers
Answer:
-1/35
Step-by-step explanation:
* means multiply
because of pemdas you should do three multiplication parts first
(1/4×2/5)+(-1/6×3/2)+(3/7×2/5)
1/20 - 3/12 + 6/35
3/60 - 15/60 + 6/35
-12/60 + 6/35
-1/5 + 6/35
-7/35 + 6/35
-1/35
Answer:
3/140
Step-by-step explanation:
1/4 × 2/5 + (-1/6) × 3/2 + 3/7 × 2/5 =
= 2/20 - 3/12 + 6/35
**********************************************
We need the LCD of 20, 12, 35.
20 = 2^2 * 5
12 = 2^2 * 3
35 = 5 * 7
LCD = 2^2 * 3 * 5 * 7 = 420
**********************************************
= 42/420 - 105/420 + 72/420
= 9/420
= 3/140
Which set of rational numbers is arranged from least to greatest? 1 over 5, −1.4, negative 1 over 2, 3
Answers
Answer:
[tex]-1.4, -\frac{1}{2}, \frac{1}{5}, 3[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{5}, -1.4, -\frac{1}{2}, 3[/tex]
Required
Order from least to greatest
We have:
[tex]\frac{1}{5}, -1.4, -\frac{1}{2}, 3[/tex]
Convert all fractions to decimal
[tex]0.2, -1.4, -0.5, 3[/tex]
Now order from least to greatest
[tex]-1.4, -0.5, 0.2, 3[/tex]
Replace fractions
[tex]-1.4, -\frac{1}{2}, \frac{1}{5}, 3[/tex]
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answers
Answer:
x ≈ 39.3°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{KL}{KM}[/tex] = [tex]\frac{6.5}{8.4}[/tex] , then
x = [tex]cos^{-1}[/tex] ([tex]\frac{6.5}{8.4}[/tex] ) ≈ 39.3° ( to the nearest tenth )
Step-by-step explanation:
Cos theta =Base/hypotenuse
Base=KL= 6.5
Hypotenuse=KM=8.4
Cos X=
[tex] \frac{6.5}{8.4} \\ [/tex]
X=
[tex] {cos}^{ - 1} \frac{6.5}{8.4} [/tex]
X=39.30 (2decimal)
Brainliest please~
Given f(x) and g(x)= f(k•x), use the graph to determine the value of k
Answers
Answer:
[tex] \displaystyle \boxed{k = 3}[/tex]
Step-by-step explanation:
to determine the Value of k we need to find the equation of f(x) and g(x)
finding the equation of f(x):
f(x) is a linear function which form is given by:
[tex] \displaystyle f(x) =mx + b[/tex]
where:
m is the slope b is the y-interceptfrom the graph we acquire that
[tex]b = 4[/tex]
to figure out m we can consider the following formula:
[tex] \displaystyle m = \frac{ \Delta y}{ \Delta x} [/tex]
from the graph we obtain that both ∆x and ∆y is 1 thus substitute:
[tex] \displaystyle m = \frac{ 1}{ 1} [/tex]
simplify:
[tex] \displaystyle m = 1[/tex]
altogether we acquire:
[tex] \displaystyle f(x) =x + 4[/tex]
finding the equation of g(x):
likewise f(x)
from the graph we obtain that
∆x=1∆y=3thus substitute:
[tex] \displaystyle m = \frac{ 3}{ 1} [/tex]
simplify:
[tex] \displaystyle m = 3[/tex]
from the graph we acquire
b=4altogether substitute therefore
[tex] \displaystyle g(x) =3x + 4[/tex]
finding the value of k:
given that,
[tex] \displaystyle \rm f(x) \: \text{and} \: g(x) =f(kx) = 3x + 4[/tex]
so our equation is
[tex] \displaystyle kx + 4 = 3x + 4[/tex]
cancel 4 from both sides:
[tex] \displaystyle kx = 3x [/tex]
divide both sides by x:
[tex] \displaystyle \boxed{k = 3}[/tex]
and we're done!
Disclaimer:
at the following link we posted the complete question
the complete question:
https://brainly.com/question/24201282Answer:
k = 3
Step-by-step explanation:
Graph is in attachment .
Finding equation of first line [ f(x) ] :-
We can see that the line passea through point ( 0,4) . Therefore ,
y intercept = 4Also it passes through (-4,0 )
Now let's find out slope .So that we can use the slope intercept form to find the equⁿ of the line.
m = y ₂ - y₁ / x ₂ - x₁ m = 4 - 0 / 0 - (-4) m = 4/4 m = 1Equation of f(x) :-
y = mx + c y = 1 * x + 4 y = x + 4 f(x) = x + 4Similarly when we will find the equⁿ of g(x) :-
y = 3x + 4g(x) = 3x + 4By question :-
f(x ) and g(x) = f ( k • x ) 3x + 4 = kx + 4 kx = 3x k = 3Could someone please help me with this question? Thanks.
Answers
Answer:
Step-by-step explanation:
MM oute le iloa
need a help!!!
I need the answer only for the c part
Please help!!
Please answer correctly
Answers
Step-by-step explanation:
316 days when you get the idea the most important thing is that the people who are looking for the right reasons why you
Which of the following is a composite number?
A. 1
B. 63
C.O
D. 19
Answers
B. 63
some simple googling would've been able to help you with this. but 0 isn't prime or composite, not sure about 1, 19 is prime, 63 is a definite composite
Solve the inequality. 2 + |t + 6| < 12
Answers
Answer:
[tex]2 + (t + 6) < 12[/tex]
[tex]2 + t + 6 < 12[/tex]
[tex]t + 8 < 12[/tex]
[tex]t < 12 - 8[/tex]
[tex]t < 8[/tex]
