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A principal P, invested 9.5% compounded continuously, increases to an amount K times the original principal after t years, where t = ln(K)/0.095.
a. Complete the table. (Round your answers to one decimal place)
K t
1
2
3
4
6
8
10
12
b. Sketch the graph of the function.
Answers
Answer:
[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12} K & t\\\cline{1-2} \vphantom{\dfrac12} 1 & 0\\\vphantom{\dfrac12} 2 & 7.3\\\vphantom{\dfrac12} 3&11.6 \\\vphantom{\dfrac12} 4& 14.6\\\vphantom{\dfrac12} 6&18.9 \\\vphantom{\dfrac12} 8& 21.9\\\vphantom{\dfrac12} 10& 24.2\\\vphantom{\dfrac12} 12&26.2\\ \cline{1-2}\end{array}[/tex]
See attachment for the graph.
Step-by-step explanation:
Part (a)Given equation for t:
[tex]t=\dfrac{\ln (K)}{0.095}[/tex]
Substitute the given values of K into the equation for t and round the answers to one decimal place:
[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12} K & t\\\cline{1-2} \vphantom{\dfrac12} 1 & 0\\\vphantom{\dfrac12} 2 & 7.3\\\vphantom{\dfrac12} 3&11.6 \\\vphantom{\dfrac12} 4& 14.6\\\vphantom{\dfrac12} 6&18.9 \\\vphantom{\dfrac12} 8& 21.9\\\vphantom{\dfrac12} 10& 24.2\\\vphantom{\dfrac12} 12&26.2\\ \cline{1-2}\end{array}[/tex]
Part (b)To sketch the graph of the given function (see attachment):
Plot the values of K along the x-axis.Plot the values of t along the y-axis.Plot the points from the table from part (a).Draw a curve through the plotted points.
Related Questions
1
message
The value of your iphone starts to depreciate/decrease as soon as you purchase it. If the function y= -200x + 1200, represents the estimated value of a certain phone after x years of ownership, what does the slope (-200) most likely represent?
The value of the phone decreases 200 dollars every year.
The current value of the phone.
The price it originally costs.
The value of the phone increases 200 dollars every year.
Answers
Answer:
-200 represents the price it orignally cost??
Step-by-step explanation:
Emily has six black marbles, ten clear marbles, and four blue marbles in a bag. If she picks one
at random, what is the probability that she will pick a black marble?
Answers
Answer:
3/10
Step-by-step explanation:
[tex]30000 \sqrt{2.85} [/tex]
Answers
Answer:
50,645.82
Step-by-step explanation:
[tex]30000 \sqrt{2.85} [/tex] =50,645.82
Squares are Rhombus but not rectangles true or false
Answers
Answer:
True
Step-by-step explanation:
Rhombus is a sideways SQUARE
Answer: True
if you turn a square 45 degrees to the side it is a rhombus
Find both the number of combinations and the number of permutations for the given number of objects.
15 objects taken 7 at a time
Answers
Answer:
First, if we have a set of K elements, such that are ordered as:
{x₁, x₂, ...}
The total number of permutations for the K elements can be found in the next way.
For the first element in the set, we have K options.
For the second element in the set, we have (K - 1) options (because we already choose one)
For the third element we have (K - 2) options, and so on.
The total number of permutation is equal to the product between the numbers of options for each position's element, then the number of permutations for K elements is:
permutations = K*(K - 1)*(K - 2)*....*2*1 = K!
Now suppose that we have a set of N elements, and we want to make groups of K elements.
The total number of different combinations of K elements is given by the equation:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
In this case we have 15 objects (then N = 15) and we take 7 at the time (Then K = 7)
Where we need to take in account the number of combinations and also the permutations for each combination.
Then the total number of different sets is:
C(15*7)*7!
First, the total number of combinations will be:
[tex]C(15,7) = \frac{15!}{(15 - 7)!7!} = \frac{15!}{8!*7!} = \frac{15*14*13*12*11*10*9}{7*6*5*4*3*2*1} = 6,435[/tex]
So we have 6,436 combinations, and each one of these combinations has 7! permutations.
permutations = 7! = 7*6*5*4*3*2*1 = 5,040
if we combine these we get:
Combinations*Permutations = 6,435*5,040 = 32,432,400
Answer:
7
Step-by-step explanation:
Find the measure of the angle indicated (x). Round to the nearest tenth Show your work to support your answer
Answers
Answer:
Karen, this type of question is such a tricky question, there is a lot of things that you just have to remember for these. Also, this type of question is asked a lot on brainly, you are in good company :P This also makes me wonder if math teachers are just REALLY BAD at teaching this.. hmmm Something is up with this type of problem b/c I have answer 100s of these type on here.. they are tricky. soooo...
Step-by-step explanation:
1st ,
Use SOH CAH TOA to recall how the trig functions fit on a triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
with the above info, we can solve your triangle :P not meant to sound "wrong" .. anyway
look for the info you are given and what you want to find... and match that to one of the 3 formulas. after you've done this a few 100 times.. you'll just remember the above formulas. :D
sooo I see that we want to find that angle ∅ and we know two of the sides and that this is a right triangle.. which means we can use the above formulas on this triangle. So we know the adjacent side and the opposite side, to the angle, soo lets use TOA
Tan(∅) = Opp / Adj
Tan(∅) = 4 / 13
now the algebra gets a little tricky here.. but it's just using the inverse function of the Tan to find the angle .. it's just going backwards with the function is all.. nothing to see here... move along.. :D
take the inverse Tan function ( arcTan) on both sides... sooo
∅ = arcTan( 4 /13 ) ( this will find the angle, but make sure your calculator is set to degrees.. and not radians )
∅ = 17.1027...°
So, now we know that angle ∅
SOH CAH TOA is super helpful for this kind of triangle problem :)
solve for x using distributive property
7(x+6)=11
and
5(x-6)=3
Answers
Tony is taking out a simple interest loan for $9,000 in order to open a skateboard shop. Which loan terms would allow Tony to pay the least amount of interest on the loan?
A. An interest rate of 7.5 % and a loan period of 2 years.
B.An interest rate of 2.5 % and a loan period of 3 years.
C.An interest rate of 2% and a loan period of 4 years.
D. An interest rate of 4% and a loan period of 5 years.
Answers
Answer
It would be C
Step-by-step explanation:
plz help I will mark brainliest if u help me
Answers
Answer:
You add up all the things it tells you... do a little more work... solve... adding up.... doing equation... The things in parenthesis you have to add up with whatever solves for X so Your answer will be... -15
The answer is... 15?!
P.s, B helps with the equation!
My first answer is 15 if i change my mind or come back and change it to solve which i will it may be different!
Tell me if i'm right!
Step-by-step explanation:
Your welcome!
Have a great week!
Byes!
-Sincerely, The Brainliest <3 :)
Plzzz guys help me ;( F(x)-mx+ b, f(-2)=3 and f(4)=1 , what is the value of m and b
Answers
Answer:
Plzzz guys help me ;( F(x)-mx+ b, f(-2)=3 and f(4)=1 , what is the value of m and
Each number in the sequence below has the same relationship to the number immediately
befor it.
ny
4, 8, 16, 32, 64,...
How can the next number in the sequence be found?
A. By adding 4 to 64
B. By adding 16 to 64
C. By multiplying 64 by 2
D. By multiplying 64 by itself
Answers
Answer:
C. By multiplying 64 by 2Explanation:
64 = 32×2
32 = 16×2
16 = 8×2
8 = 4×2
(so 128 is the next number)
Answer:
c by multiplying 64 by 2
Step-by-step explanation:
in the sequence we can see that 4×2=8 8×2=16 16×2=32 32×2=64 64×2=128
solve inequality -8x < 32
Answers
Answer:
x > -4
Step-by-step explanation:
I just looked it up
But I know this is it
Answer:
Inequality Form:
x > − 4
Interval Notation:
(-4,∞)
Step-by-step explanation:
I need help with my math assignment
Answers
Answer:
63
Step-by-step explanation:
×+15+102=180
×=180-102-15
×=64
Order them from least to great
Answers
Answer:
-21/2 <-5/2 < - 2 < - 1.75 <-1 <1.75 <9/4
Which expression is equivalent to
(5^-2) (5^-4)?
A. -1/125
B. -1/5
C. 1/125
D. 1/5
Answers
Answer:
umm none the above cuz 5^-2 = 1/25 and 5^-4 = 625, 625*25 = 15625 so 1/15625 bru
Step-by-step explanation:
Help math pls??? Look at picture for equation
Answers
please help!!!!!!!!!!!
Answers
Help please will mark brainliest!!!
Answers
Answer:
9 times 2 because of the 2 sides meaning... the answer is... 18 but also had to round it up to 20 because it's higher than 5 its 2 left but if necessary i think you need to add 9 more on the other side with the 9 across and do the same with the 2 mi!
Step-by-step explanation:
Hope i helped! Your welcome! Have a great week!
HELP ASAP What is the distance between the following points
Answers
Answer:
6
Step-by-step explanation:
What is the volume of a hemisphere with a radius of 9.8 in, rounded to the nearest tenth of a cubic inch?
Answers
Answer:
the volume of the hemisphere is 1970.2 cubic inches.
Step-by-step explanation:
The given is,
Radius of hemisphere is 9.8 inches.
Step:1
Formula of volume of hemisphere is,
..................(1)
Where,
r - Radius of hemisphere
Step:2
From the given,
r = 9.8 inches
Equation (1) becomes,
=
=
= (0.66666666)(3.1415)(942.192)
= 1971.23
Volume of hemisphere = 1971.23 cubic inches
Result:is 1970.2 cubic inches.
Answer:
1971.2
Step-by-step explanation:
I just did it and got it right, it's not 1970.2, trust me
What is the answer please help if you give me a link I will report sorry not sorry
Answers
Answer: 4.5
Step-by-step explanation:
You add all the number and divide them by the amout
of numbers there are for example here you add them all and get 45 and since there are 10 you divide 45 by 10 and get 4.5
Solve the system of equations using the substitution method.y=2,2x+y=8
Answers
Answer:
x=3
Step-by-step explanation:
2x+2=8
2x=6
x=3
Answer:
x=3, y=2
Step-by-step explanation:
y=2
substitute 2 for y
2x+2=8
x=3
Simplify
8(10 m)
80 + m
18 m
80 m
810 m
Answers
80m, you kind of distribute so 8 times 10m is 80m
5 COINS AND CROWNNNNNN PLEASEEEEE FIND X AND Y, I NEED THIS SO BAD PLEASE SHOW WORK, I WILL GIVE BRAINLEST
Answers
Answer: change 9x and 5x
Step-by-step explanation:
What is the square root of pie?
Answers
Answer:
The square root of Pi is approximately 1.77245.
Step-by-step explanation:
Answer:
About 1.77245.
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options.
Answers
Answer:
A, C, D.
Step-by-step explanation:
PLZ HELP!
Find the 19th term in the geometric sequence.
2, 6, 18, 54, ...
A)2,324, 522,934
B)1, 162, 261,467
C)6,973,568,802
D) 774, 840,978
Answers
Answer:
D
Step-by-step explanation:
The equation for the sequence turns out to be 2([tex]3^{n-1}[/tex]) where n is the nth.
Plugging in 19 you get 2([tex]3^{18}[/tex]), or 774,840,978
Carter wants to buy a CD for $16. If there is 7% sales tax, what is the amount of tax Carter will have to pay?
Answers
Answer:
$1.12
Step-by-step explanation:
7% of 16 is 1.12
The periscope of a submarine is at sea level. The boat captain spots an airplane with
an elevation angle of 30°. The airplane is flying at an altitude of 2000 feet.
The straight line distance between the submarine and the airplane is...
Answers
Answer:
The airplane is 100.4 flying at an altitude of 30,000 feet. AB = 210,000 feet. At what angle is the plane descending (the angle of depression)?. Above is a picture of astronauts ...
7 pages·477 KB
The straight line distance between the submarine and the airplane is 4000 feet.
What is trigonometric ratio?Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let d represent the straight line distance between the submarine and the airplane. Hence:
sin(30) = 2000/d
d = 4000 feet
The straight line distance between the submarine and the airplane is 4000 feet.
Find out more on trigonometric ratio at: https://brainly.com/question/24349828
Check all statements that are true.
a. Adding two integers and then taking the remainder produces the same result as taking their remainders first, then adding them, and then applying the remainder operation once more.
b. Saying that a divides b is the same as saying that b is a multiple of a.
c. Adding two integers and then taking the remainder produces the same result as taking their remainders first and then adding them.
d. When you perform division by 5 with remainder, the remainder is an integer from -5 to 5.
e. If an integer a divides a product of two integers b and c, then a must divide b or a must divide c.
f. If an integer divides two numbers, it also divides their difference.
g. If an integer divides two numbers, it also divides their sum.
h. When you perform division by 3 with remainder, the remainder is one of the integers 0,1,2.
i. If a and b are positive integers, and a = bq + r is the decomposition of a given by the division algorithm, then q can be found as the floor of a/b, and then r can be found as r = a - bq.
j. If an integer a divides an integer b, then a also divides any multiple of b.
Answers
Answer:
a. True
b. True
c. False
d. False
e. False
f. True
g. True
h. True
i. True
j. True
Step-by-step explanation:
When the integer divides the two number then their sum is also divisible by that integer. This is also the case in the subtraction when two number are divisible then their difference is also divisible. When there is division by 5 the number not necessarily can be 5 or -5. This statement is not correct.