By what factor does the output value increase as each input value increases by 1
Answers
Given:
The table of values of an exponential function.
To find:
The factor by which the output value increase as each input value increases by 1.
Solution:
The general exponential growth function is
[tex]f(x)=ab^x[/tex] ...(i)
where, a is initial value and b is growth factor.
From the given table it is clear that the function passes through (0,3). So, put x=0 and f(x)=3 in (i).
[tex]3=ab^0[/tex]
[tex]3=a(1)[/tex]
[tex]3=a[/tex]
From the given table it is clear that the function passes through (2,12). So, put a=3, x=2 and f(x)=12 in (i).
[tex]12=3b^2[/tex]
Divide both sides by 3.
[tex]4=b^2[/tex]
Taking square root on both sides, we get
[tex]\pm \sqrt{4}=b[/tex]
[tex]\pm 2=b[/tex]
Growth factor cannot be negative. So, b=2.
Therefore, the output value increase by factor 2 as each input value increases by 1.
Related Questions
A computer company has 1030 computers in two different warehouses. Warehouse A has 150 more computers than Warehouse B. How many computers are in Warehouse B?
Answers
Answer:
880
Step-by-step explanation:
Mrs. Afonso is competing in a race in which she both runs and rides a bike. She runs 5 kilometers in 0.5 hours and rides her bike 20 kilometers in 0.8 hours. At the rate given, how many kilometers can she run in one hour?
Answers
Answer:
Step-by-step explanation:
If Mrs. Alfonso runs 5 km in 0.5 hours,
she will run 10 km in an hour
Sandy went to 20 baseball games this year. She went to 26 last year. How many baseball games did Sandy go to in total?
Answers
20 + 26 = 46
can you do this please
Answers
Answer:
x = 24
Step-by-step explanation:
ABCD is a parallelogram.
Angle B and Angle C are adjacent (successive) angles.
Adjacent angles of a parallelogram are supplementary.
Therefore,
[tex](5x) \degree + (2x + 12) \degree = 180 \degree \\ \\ (5x + 2x + 12) \degree = 180 \degree \\ \\ (7x+ 12) \degree = 180 \degree \\ \\7x+ 12 = 180 \\ \\7x = 180 - 12 \\ \\ 7x = 168 \\ \\ x = \frac{168}{7} \\ \\ x = 24[/tex]
[tex]\boxed{\pink{\sf\leadsto Value \ of \ x \ is \ 24^{\circ}}}[/tex]
[tex]\boxed{\pink{\sf\leadsto Value \ of \ \angle C \ is \ 60^{\circ}}}[/tex]
[tex]\boxed{\pink{\sf\leadsto Value \ of \ \angle D \ is \ 120^{\circ}}}[/tex]
Step-by-step explanation:A parallelogram is given to us . in which m ∠ B = 5x and m ∠C = 2x + 12 ° . And we need to find x .
Figure :-
[tex]\setlength{\unitlength}{1 cm}\begin{picture}(12,12)\thicklines\put(0,0){\line(1,0){5}} \put(5,0){\line(1,2){2}}\put(7,4){\line( - 1,0){5}}\put(2,4){\line( - 1, - 2){2}}\put(0,-0.4){$\bf A$}\put(5,-0.4){$\bf b$}\put(6.5,4.3){$\bf c$}\put(2,4.3){$\bf d$}\qbezier(4.4,0)( 4.5, 0.8)(5.22,0.54)\put(4,0.4){$\bf 5x$}\put(4.7,3.3){$\bf 2x + 12$}\end{picture}[/tex]
Q. no. 1 ) Find the value of x.
Here we can clearly see that ∠DCB and ∠ABC are co - interior angles . And we know that the sum of co interior angles is 180° .
[tex]\tt:\implies \angle DCB + \angle ABC = 180^{\circ} \\\\\tt:\implies (2x + 12)^{\circ} + 5x^{\circ}=180^{\circ} \\\\\tt:\implies 7x = (180 - 12 )^{\circ} \\\\\tt:\implies 7x = 168^{\circ} \\\\\tt:\implies x =\dfrac{168^{\circ}}{7} \\\\\underline{\boxed{\red{\tt\longmapsto x = 24^{\circ}}}}[/tex]
Hence the value of x is 24° .[tex]\rule{200}2[/tex]
Q. no. 2 ) Determine the measure of < C .
Here we can see that <C = 2x + 12 ° . So ,
[tex]\tt:\implies \angle C = 2x + 12^{\circ} \\\\\tt:\implies \angle C = 2\times 24^{\circ} + 12^{\circ} \\\\\tt:\implies \angle C = 48^{\circ} + 12^{\circ} \\\\\underline{\boxed{\red{\tt\longmapsto \angle C = 60^{\circ}}}}[/tex]
Hence the value of <C is 60° .[tex]\rule{200}2[/tex]
Q. no. 3 ) Determine the measure of < D .How you determined the answer .
Here we can clearly see that ∠D and ∠C are co - interior angles . And we know that the sum of co interior angles is 180° .
[tex]\tt:\implies \angle C + \angle D = 180^{\circ} \\\\\tt:\implies 60^{\circ} + \angle D = 180^{\circ}\\\\\tt:\implies \angle D = 180^{\circ} - 60^{\circ} \\\\\underline{\boxed{\red{\tt\longmapsto \angle D = 120^{\circ}}}}[/tex]
Hence the value of <D is 120° .Please help!!!!
Tom, Lisa, and Jane are competing in a cooking competition. They all used different amounts of sugar from a can containing 4 pounds of sugar. Tom used 13% of the total sugar in the can. Lisa used 0.6 pounds of the total sugar in the can. Jane used 0.12 of the total sugar in the can. Who used the greatest amount of sugar from the can? Show your work and explain your answer in words.
Answers
Answer:
13 x 4
100
= 0.52 so tom used the most
Step-by-step explanation:
4. At a certain time of day, an 18-foot pole casts a shadow that forms an angle of 50° with the
ground. How long is the shadow?
Answers
Step-by-step explanation:
Opposite to the angle = Pole
Adjacent to the angle = Shadow
Therefore tan50° = 18ft/x,
x = 18ft / tan50° = 15.1ft.
One-sixth of the 24 children in the park are playing soccer. How many children are playing soccer in the park?
Answers
Answer:
Step-by-step explanation:
children playing in park = (1/6)*24 = 4
One-sixth of the 24 children in the park are playing soccer. How many children are playing soccer in the park?
24 children (whole
12 children (half
8 children (third
6 children (quarter
4 children (sixth
1000:150:600 simplified
Answers
Answer:
20:3:12
Step-by-step explanation:
1000:150:600
divide all the numbers by 50= 1000÷50 : 150÷50 : 600÷50
= 20:3:12
A bag of 12 apples is most likely to weight
Answers
Answer:2.5kg
Step-by-step explanation:
A baby was born with a weight of 5 pounds and then began to gain 1.25 pounds per month. Write an equation for W,W, in terms of t,t, representing weight, in pounds, of the newborn baby tt months after birth.
Answers
Answer:
1.25t+5
Step-by-step explanation:
periodpointblankif the cost of 4 kg of rice is rupees 90,then how much rice is purchased with rupees 247.50
Answers
Answer: 11
Step-by-step explanation:
90 : 4 = 22.5
247.50 : 22.5 = 11
hope is helps * hugs ✨
Multiply 2.3. (-1.2)
Answers
Answer:
-2.76
Step-by-step explanation:
2.3x(-1.2)
= -2.76
what is the equation that passes through the point (3,-6) and has a slope of 3/4?
Answers
Answer:
lol
Step-by-step explanation:
Some oone idea about this ??
N = {X:X
is an odd number, 21<x<3
XEN]
Answers
It seems to be that the Roster form would do not do anything but the thing is that this listing would give us the output of a set from this problem.
Your answer would be, N = Set of Odd Numbers such that x is greater than 21 and less than or equal to 35 = {23, 25, 27, 29, 31, 33, 35}.
Greg and Kevin both travel between two towns that are 90 miles apart. Greg travels and it takes him 1 hour 30 minutes. Kevin cycles and it takes him 7 hours 30 minutes. Work out the difference between the average speed.
Answers
Answer:
48 miles/hour
Step-by-step explanation:
The average speed is the ratio of the total distance traveled to the total time taven, it i given by the formula:
Average speed = total distance / total time
For Greg, the total distance = 90 miles and the total time = 1 hour 30 minutes = 1 hour + (30/60) hour = 1.5 hours. Hence:
Average speed = 90 / 1.5 = 60 miles/hour
For Kevin, the total distance = 90 miles and the total time = 7 hour 30 minutes = 7 hour + (30/60) hour = 7.5 hours. Hence:
Average speed = 90 / 7.5 = 12 miles/hour
Difference between the average speed = 60 miles/hour - 12 miles per hour = 48 miles/hour
A cheetah can run a rare of 105,600 years per hour find the number of miles the cheetah could run at this rate in 5 minutes.
Answers
Answer:
360 yards per 5 minutes.
Step-by-step explanation:
A cheetah can ride up to 105,600 yards per hour.
An hour is equal to 60 km.
It can run up to 'x' miles per 5minutes.
So, 360 x 5/ 5
= 1800/5
= 360 yards per 5 minutes.
HOPE THIS HELPS !!
PLS HELP
identify the slope and the y-intercept in the following equation
y=1/2x+3
Answers
explanation- the original format is y=mx+b. when identifying the parts, m=slope and b=y intercept. so when you look at it, you find where those numbers are
5. Which of the following equations is in standard form?
a. 2x = 7
b. -3x + 2y = 10
c. y - 3 = x
d. y + 5 = 4 (x - 4)
Answers
Answer:
the answer is B
Step-by-step explanation:
whoever comments first gets brainliest and whoeverelse answers gets 50 points cause why not 2=2=3=4=5=6=7=8=9=0+12345-7=9(so it doesn't get taken down)
Answers
Answer:
Yo whats up
Step-by-step explanation:
I win and im the brainlest.
What value of b will cause the system to have
infinite number of solutions?
y=6x-b
-3x + y=-3
b=
O 2
O 4
O6
O8
Answers
9514 1404 393
Answer:
6
Step-by-step explanation:
The value of b that makes the two lines identical is the opposite of the y-intercept of the line.
y = 6x -6 . . . . has y-intercept = -6
The value of b is the number in the term -6, so is 6.
An oil-well contractor drills a shaft 7 meters deeper into the ground every 2 hours. Which graph has a slope that best represents this rate?
Answers
Answer:
Graph G
Step-by-step explanation:
The graphs are attached
Given that the oil-well contractor drills a shaft 7 meters deeper into the ground every 2 hours, hence the rate at which the shaft drills = 7 meter / 2 hours = 3.5 meters per hour
Since the drill goes into the ground, hence the rate is negative that is -3.5 meters per secong
The slope (rate of change) of a line (m) is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
a) For graph F, the line passes through the point (0,0) and (10, -20). Hence:
[tex]Slope\ of\ line\ F=\frac{-20-0}{10-0} =-2\ meters\ per\ second[/tex]
b) For graph G, the line passes through the point (0,0) and (10, -70). Hence:
[tex]Slope\ of\ line\ G=\frac{-70-0}{10-0} =-7\ meters\ per\ second[/tex]
c) For graph H, the line passes through the point (0,0) and (10, -35). Hence:
[tex]Slope\ of\ line\ H=\frac{-35-0}{10-0} =-3.5\ meters\ per\ second[/tex]
d) For graph J, the line passes through the point (0,-3.5) and (10, -3.5). Hence:
[tex]Slope\ of\ line\ j=\frac{-3.5-(-3.5)}{10-0} =0\ meters\ per\ second[/tex]
Answer:The answer is H , It is the graph where -10 is right below the 0 on the y.
What is the answer to y=-4/8x+9? PLEASE send your helping hands!!
Answers
Answer:
x=−2y+18
Step-by-step explanation:
if you want to graph it then click on the screenshot
(ps tell me if this helped)
The audience thinks 30\%30%30, percent of Brandon's jokes are funny.
What fraction of Brandon's jokes does the audience think are funny?
Answers
Answer:
3/10
Step-by-step explanation:
Brandon's jokes does the audience think are funny = 30%
What fraction of Brandon's jokes does the audience think are funny?
Express the percentage as a fraction
= 30%
= 30 / 100
= 3/10
The fraction of Brandon's jokes that the audience think are funny is 3/10
100 points please help
Answers
Answer:
d
Step-by-step explanation:
it is not the right graph
Answer:
THe answer is the 4th one/the graphed picture
Step-by-step explanation:
The reason is because the fourth picture is not correctly graphed
10. A bag contains 4 red balls, 6 green balls and some white balls. If the probability of not drawing a white ball in one draw be \(\frac{2}{3}\) then find the number of white balls.
Answers
Answer:
No of white balls = 5
Step-by-step explanation:
Given that,
Total no of red balls = 4
Total no of green balls = 6
The probability of not drawing a white ball in one draw be, [tex]P=\dfrac{2}{3}[/tex]
We need to find the number of white balls. Let there are x balls.
The probability of drawing a white ball = 1 - the probability of not drawing a white ball
= 1 -2/3
= 1/3
Using the formula for solving probability of having a white ball.
[tex]P=\dfrac{\text{favorable outcome}}{\text{total no of outcomes}}\\\\\dfrac{1}{3}=\dfrac{x}{4+6+x}\\\\\dfrac{1}{3}=\dfrac{x}{10+x}\\\\10+x=3x\\\\10=2x\\\\x=5[/tex]
Hence, there are 5 white balls.
What does this mean? Its REALLY important I get this right.
Answers
The correct answer is Option A
[△SRT]
Answer:
[tex]\triangle{SRT}[/tex]
Step-by-step explanation:
You can eyeball this question and you can easily see that [tex]\angle{R}=\angle{M}[/tex] and [tex]\angle{S} = \angle{N}[/tex] so then the answer would be [tex]\triangle{SRT}[/tex]
Line a passes through that point (-8,-7) and has a slope of 5/8. Choose the equation that best represents A
Answers
Answer:
y = 5/8 x -2
Step-by-step explanation:
Given that the slope of the line, m=5/8, which passes through the point (-8,-7).
Let the equation of the line be y=mx+c
where m is the slope of the line and c is a constant.
As m=5/8, so the equation of line become
y= 5/8x+c
As the line passes through the point (-8,-7), so putting y= -7 and x= -8, we have
-7 = 5/8(-8)+c
-7 = -5 + c
c= -7 + 5
c= -2
On putting the value of c, the equation of line become
y=5/8 x -2
Hence, the equation of the line is y = 5/8 x -2.
Damian bought a box of raisins that weighed 40 ounces. How many pounds of raisins did Damian buy?
2 1/2
3
3 1/2
4
Answers
Answer: Your asnwer is 2.5 lbs Can i have branliest?
Step-by-step explanation:
you invested $800 for 2 years at an interest rate of 4.5%. What was the interest earned on your investment?
Answers
Answer:
$72
Step-by-step explanation:
Interest = Principal(Rate)(Time)/100
Interest = $800(2)(4.5)/100
Interest = 7200/100
Interest = $72 (Answer)
A recipe requires 8 cups of baking powder. You can only measure using 2/3 cups.
Answers
Answer:
sorry to tell you this but you will be measuring for a while
Step-by-step explanation:
go to walmart get a 2/3 measuring cup and measure out 8 cups i guess. get me some chips while your there plss. <3