The graphs below show four functions.
Which graph best shows the function f(x) = 3(3)−x to represent the rate at which a radioactive substance decays?
a
Graph A
b
Graph B
c
Graph C
d
Graph D
Answers
The graph that best models the exponential function [tex]f(x) = 3(3)^{-x} = \frac{3}{3^x}[/tex] is graph A.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value, that is, the value of y when x = 0.b is the rate of change.In this problem, the function is:
[tex]f(x) = 3(3)^{-x} = \frac{3}{3^x}[/tex]
The initial value is:
[tex]f(0) = \frac{3}{3^0} = 3[/tex]
The x in the exponent is negative, which means that it is a decaying function, hence graph A is correct.
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
Related Questions
The altitude of an isosceles triangle bisects the base and measures 10ft. If the base of the triangle measures 16ft, calculate: a) the area of the triangle b) and one side of the triangle.
Answers
Answer:
Step-by-step explanation:
the formula for calxulating the area if the isosceles triangle is expressed as;
[tex]A = \frac{1}{2}bh[/tex]
b is the base of the triangle
h is the altitude
Given
b = 16ft
h = 10ft
Substitute
A = 1/2 * 16 * 10
A = 8*10
A = 80ft²
Hence the area of the triangle is 80ft²
b) To get the measure of one side of the triangle, we will use the pythagoras theorem. Let s be the slant side
s² = h²+(b/2)²
s² = 10²+(16/2)²
s² = 10²+(8)²
s² =100+64
s² =164
s = √164
s = 12.8ft
Hence one side of the triangle is 12.8ft
Can you help me with this question
Answers
You put a frozen pizza in the oven. After 20 minutes,
you take it out. Let T(m) be the temperature of the pizza m
minutes after you place it in the oven. Explain the meaning
of each statement.
I
T(0) = 35
T(15) >T(5)
T(m) = 100
Answers
T(t) = temp at any given time t = time. To = initial temp of the heated object ... A cake removed from the oven has a temperature of 210°F It is left to room that has a temperature of 70°F. After 30 minutes, the temperature of in is 140°F a. Use Newton's Law of Cooling to find a model for the temperatur ... 20 = 1402 -0.02317.
Please help! Last question and it was due last night! Will choose brainiest!
Answers
Answer:
YZ=6.42 m<Y=12
Step-by-step explanation:
Answer:
77 degrees yz
IF YOU ANSWER THIS I WILL LOVE YOU FOREVER THNXX I DIDN'T STUDY ON ACCIDENT I HAS SOFTBALL PRACTICE
Answers
Answer:
8
Step-by-step explanation:
15 divided by 6 is 2.5
20 divided by 2.5 is 8
Answer:
Step-by-step explanation:
to answer this question, you need to set up a preportion.
15 = 6
20 x
then we would multiply 15 by x, and 20 by 6.
20(6) = 120
120= 15x
120 divided by 15 is:
x= 8
Attend to precision. Suppose that 21 and 22 are same-side interior angles formed by two parallel lines cut by a transversal, and that mZ1 = 7x - 4 and m2 = 20x – 5. a. What is the value of x? answer b. What is mi? answer c. What is mx2? answer d. Explain how you found your answers. answer
Answers
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Simplify the expression:
3x2 - x + 7 + 5x + 2 - 2x2
Answers
4x + 6 + 7+ 2 - 4
4x + 11
Answer: yes
Step-by-step explanation:
3 x 2 - x + 7 + 5 x + 2 - 2 x 2
6 - x + 7 + 5x + 2 - 4
6 + 7 + 2 - 4 - x + 5x
13 - 2 + 4x
11 + 4x
Solve the equation for y.
12 13 y + 12 = 1/3 - 20
-32
-80
-320
320
Answers
Answer:
No
Step-by-step explanation:
sorry iiiiiimmm bad at math
I'LL GIVE BRAINLIEST! What similarity property, if any, can be used to show that the following two triangles are similar. A) SAS B) Not enough information given C) SSS D) AA
Answers
Answer:
SSS
Step-by-step explanation:
They have the same ratio
Joe borrowed $6,000 from the bank at a rate of 7% simple interest per year. How much interest did he pay in 4 years?
Answers
Answer:
Joe would be paying $700 in 5 years time.
Step-by-step explanation:
Answer:
In 4 years Joe would have to pay $1,680 in simple interest.
Step-by-step explanation:
So first of all you want to start by finding what P, r and t would be.
P = Principal amount ($$)
r = interest rate (%)
t = time
Once I found all of those I put them into the equation (l = Prt) and solved. That is how I came up with my answer. Check the screenshot provided to see what P, r and t would be and to see all my work! :)
Have a great day!
Nathan is using his grandmother's recipe to make pies
On Monday, he used 15 3/4 cups of sugar to make 9 pies
On Tuesday, he used 23 3/4 cups of sugar to make 13 pies
Which of the following must be true? (Select all that apply)
A) He used 1 cup of sugar for every 1 3/4 pies he made
B) He would use 14 cups of sugar to make 8 pies
C) The number of cups of sugar is proportional to the number of pies he made because he used the same number of cups of sugar for each pie
D) The number of cups of sugar is not porptional to the number of pies he made because the increase in the number of cups of sugar between Monday and Tuesday is greater than the increase in the number of pies
E) if Nathan uses 8 3/4 cups of sugar to make 5 pies on Wednesday and then graphs the points, for all the three days, to represent the relationship between the cups of sugar used and the number of pies made, the points would not fall on a straight line
Answers
Answer:
its a & c
Step-by-step explanation:
Edin has £300 in his saving account his bank offers his a fixed 5% simple interest rate per annum for a period of 3 years how much interest will he have earned after 3 years ?
Answers
Answer:
45
Step-by-step explanation:
The simple interest formula is
I=p×r×t
I interest earned?
P principle 300
R interest rate 0.05
T time 3years
So
I=300×0.05×3
I=45
interest will he have earned in 3 years is 45
Question 2
2.5 pts
A firefighter sees a woman trapped in a building 91 feet up from the bottom floor. If the
firetruck is parked 67 feet away from the bottom of the building, at what angle of elevation, to
the nearest degree, should the firefighter extend the ladder to reach the woman?
Previous
Answers
Answer:
The firefighter should extend the ladder at 54° of elevation.
Step-by-step explanation:
Trigonometric Ratios
The ratios of the sides of a right triangle are called trigonometric ratios. There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant, and cotangent.
The longest side of the triangle is called the hypotenuse and the other two sides are the legs.
Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.
Tangent Ratio:
[tex]\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]
The woman is trapped at 91 feet up from the ground, and the firetruck is 67 feet away from the building.
The wall, the ground, and the ladder form a right triangle, where θ is the horizontal angle of the ladder.
Being the height of the woman the opposite leg and the distance where the firetruck is parked, the adjacent leg:
[tex]\displaystyle \tan\theta=\frac{91}{67}=1.3582[/tex]
The angle is calculated as the inverse tangent:
[tex]\theta=arctan(1.3582)\approx 54^\circ[/tex]
The firefighter should extend the ladder at 54° of elevation.
What is the value of the underlined digit?
5,682, 450,003
A. eighty thousand
B. eighty million
C. eighty-two million
D. eighty billion
Answers
HELP ASP!!❤️
WILL GIVE BRAINLIEST!...
Find the slope of the line. Enter your answer in simplest form.
Answers
Answer:
[tex]m=\frac{-4}{3}[/tex]
General Formulas and Concepts:
Order of Operations: BPEMDASSlope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (-6, 5)
Point (3, -7)
Step 2: Find slope m
Substitute: [tex]m=\frac{-7-5}{3-(-6)}[/tex]Simplify: [tex]m=\frac{-7-5}{3+6}[/tex]Subtract/Add: [tex]m=\frac{-12}{9}[/tex]Simplify: [tex]m=\frac{-4}{3}[/tex]Answer:
the slope is -4/3
Step-by-step explanation:
m=y2-y1/x2-x1
-7-5=(-12)
3-(-6)=9
-12/9
-12/3=(-4)
9/3=3
-4/3
hope this helps :3
if it did pls mark brainliest
Michaela signs up for a package of 6 dance classes for $29.95, and each additional dance class is $3.95.
Which expression shows how much she pays for d dance classes when d 2 6?
A. 29.95 + 3.95d
B. 29.95 + 3.95(d-6)
C. 29.95 : 0 + 3.95
D. 29.95 = (d - 6) + 3.95
Answers
Because 29.95 + 3.95 (d) as per dance class?
5/3x - 2y=-2
-x+y=2
Answers
Answer:
(6/11, 16/11)
Step-by-step explanation:
While it's fairly obvious that you're supposed to "solve this system of equations," it'd be clearer if you were to say so specifically. Also, reduce ambiguity by using parenthes: You meant either (5/3)x or 5/(3x). Which one? I'm assuming it's (5/3)x.
Then our system is:
(5/3)x - 2y = -2
x + y = 2
Let's eliminate y through addition/subtraction. Multiply the 2nd equation through by +2:
(5/3)x - 2y = -2
2x + 2y = 4
------------------------
(11/3)x = 2
Multiplying both sides by 3 eliminates the fractional coefficient:
11x = 6
Then x = 6/11. Now we must solve for y:
-(6/11) + y = 2
Multiplying 2 by 11/11 yields:
-(6/11) + y = 22/11.
This simplifies to y = 16/11
Thus, the solution of this system is
(6/11, 16/11)
Work out the sum of 8.2 and 949.65.
Answers
Answer:
957.85
Step-by-step explanation:
949.65
+ 8.2
_________
957.85
NoAnswer:
Step-by-step explanation:
949.65
+. 8.20
=957.85
Sum is 957.85.
\text{Nine times the difference of 8 and a number.}
Nine times the difference of 8 and a number
Answers
Answer:
9x8=72 72-8=64 64x9=576
Step-by-step explanation:
Answer:
Nine times the difference of 8 and a number = 9(x-8)
1)50% of 60 2) 8 out of 80 is what percent?
Answers
Answer:)
1) 50% of 60 is 30
2) 8 out of 80 is 10%
You're welcome :)
Answer:1. 30
2. 10%
Step-by-step explanation:
help please! i'll be sure to mark brainliest if i'm able to!
Answers
Answer: its the first 3 i think
Step-by-step explanation:
Answer:they are not congruent
Step-by-step explanation:
(02.01 LC) Solve:negative 1 over 2 x + 2 = −x + 7 (5 points)??.?.??????
Answers
Answer:
x=10
Step-by-step explanation:
let me know if correct
Answer:
x=10
Step-by-step explanation:
Kara earned $136.75 last week working 16 hours. She earned $10.50 per hour at the fast food restaurant and $4.25 per hour helping her aunt clean her store. how many hours did she work at the fast food restaurant ? how many hours did she help her aunt clean the store ?
Answers
Answer:
ANSWER: she worked 11 hours at the fast food restaurant and 5 hours helping her aunt
Step-by-step explanation:
First we are going to try to find how many hours she worked on the fast food restaurant so you multiply 4.25 time 16 and x
10.50x + 4.25(16-x) =136.75
10.50x + 68 - 4.25x= 136.75
Then, you subtract 68 from both sides and subtract 4.25x from 10.50x
6.25x=68.75
Divide
X=11 that is how many hours she worked at the FAST FOOD RESTAURANT
Then 16-11 and that gives us how many hours she helped her aunt.
help I want to get sleep
Answers
Answer:
I got -45.1 but idek if its right or not
Answer:
-45.1
Step-by-step explanation:
-6*7.1 + 2.5
-42.6 + 2.5
= -45.1
15) In the proof: STATEMENT: e / f REASON: 15)
Transitive Property of Congruency
Converse of AEA Theorem
AEA Theorem
AIA Theorem
Definition of Congruent Angles
Answers
Answer:
Can you be more specific if you can I will answer in the comments :)
Step-by-step explanation:
The highest elevation in a small country occurs on a mountain 1232 meters above sea level, while the lowest elevation in the same country occurs at -27 meters (below sea level). What is the difference in elevation between the highest and lowest points?
Answers
Answer: 1259 meters
Step-by-step explanation:
Highest elevation = 1232 meters
Lowest elevation = -27 meters
The difference in elevation between the highest and lowest points will be:
= 1232 - (-27)
= 1232 + 27
= 1259 meters
Note that (-) × (-) = +
may someone please help me with this im confused
Answers
Answer:
d
Step-by-step explanation:
Will give brainlist!
options:
>s~>u
segment sc~segment cu
segment cb~segment cb
segment sb~segment bu
definition of a segment bisector
vertical angles congruence theorem
reflexive property
definition of an angle bisector
Answers
Vertical angles theorem states that vertical angles, angles that are opposite to each other and formed by two intersecting straight lines, are congruent.
Where is the function decreasing?
A.-3 < x < 1
B.-∞< x < -3 and 1 < x < 4
C. 1 < x < 4
D.-∞< x < 1
Answers
Answer:
A. -3 < x < 1
General Formulas and Concepts:
Reading a Cartesian PlaneAnalyzing a GraphStep-by-step explanation:
"When is the function decreasing" is saying when the graph is going down.
Calculus-wise, we are finding when the slope of the tangent line is negative.
From the graph, we see it decreasing from -3 to 1. Everywhere else is increasing.
Therefore, our interval decreasing is from (-3, 1).
How to make this question..?
