Given:
The exponential function passes through two points (0,4) and (3,32).
To find:
The formula for the exponential function.
Solution:
The general form of an exponential function is
[tex]y=ab^x[/tex] ...(i)
where, a is initial value and b is growth factor.
The exponential function passes through two points (0,4) and (3,32). It means the function must be satisfy by these points.
Putting x=0 and y=4 in (i), we get
[tex]4=ab^0[/tex]
[tex]4=a(1)[/tex]
[tex]4=a[/tex]
Putting a=4, x=3 and y=32 in (ii), we get
[tex]32=4b^3[/tex]
Divide both sides by 4.
[tex]8=b^3[/tex]
Taking cube root on both sides.
[tex]2=b[/tex]
Putting a=4 and b=2 in (i), we get
[tex]y=4(2)^x[/tex]
Therefore, the required formula for the exponential function is [tex]y=4(2)^x[/tex].
Is the graph below proportional? Explain.
500
400
300
Total cost ($)
200
100
0 2 4 6 8 10
Time (h)
Answer:
50/1
Step-by-step explanation:
x=1,2,3
y=50,100,150
y/x=50/1
I don’t get this please help me
Answer:#1: 1225
#2: 1149
Step-by-step explanation:
Hope this helps! :) ❤❤❤
Type ALL the steps of writing the equation of the line given the slope of the line is −4 and a point on the line is (−2,1).
Answer:
y = -4x - 7
Step-by-step explanation:
we use the slope intercept formula given by; y = mx + b
b = y intercept, which is when x = 0
m = slope
so they tell us the slope.. we just need to find b - the y intercept.
y = mx + b
plug in your coordinates (-2,1)
1 = -4(-2) + b
1 = 8 + b
1 - 8 = b
-7 = b
put it all together.
y = -4x - 7
Melanie worked last weekend at her part-time jobs. She
earned $67.60. Place an X in the appropriate cell for
each row to indicate whether each situation represents
the additive inverse of how much Melanie earned last
weekend.
Additive Inverse
Not Additive
Inverse
finding $67.00
lo sin g $67.60
spending 567.60
recieving a gift of 67.00
Answer:
Step-by-step explanation:
HadsRIC
Which one A,B,C,D This times so I need a answer in a hurry
Answer:
um c? i think so, i dont rly know
Step-by-step explanation:
Bill and Ted are each saving money for a trip to Europe. Bill started with $75 and saves an additional $15 per week. Ted began with $120 and saves an additional $10 per week. After how many weeks, x, will they have the same amount of money saved? Explain how you arrived at your answer.
Answer:
9 weeksStep-by-step explanation:
After x weeks Bill will save money:
75 + 15xAnd Ted will save:
120 + 10xSince they save same amount, we have equation:
75 + 15x = 120 + 10x15x - 10x = 120 - 755x = 45x = 45/5x = 9 weeksA house increased in value by 36 percent since it was purchased. If thw current value is 306000 what was the value when it was purchased
What is the area in square feet 6.3ft, 8ft
Answer:
go to my account and answer the latest question and say lol u dont
have to answer it tho just put lol for 25 free points.
Step-by-step explanation:
Answer:
50.4
Step-by-step explanation:
Which set of ordered pairs
represents a function?
A. (5,-8),(8,-1),(8,7),(-4,2)
B. (-9,-9),(7,-9),(-7,-7),(9,-8)
C. (4,7),(-7,-4),(6,8),(-7,6)
D. (0,8),(-7,2),(4,-9),(4,-3)
Answer:
C. (4,7), (-7, -4), (6, 8), (-7, 6)
Step-by-step explanation:
There are no repeating numbers. For example, in answer A, 8 is repeated, (8, -1) and (8, 7)
Hope that helped! If you have any questions, just ask!
Help plz it’s 50 points help
Answer:
Step-by-step explanation:
Answer:
frist answer is right
Step-by-step explanation:
9X3 + 9 X 2 -43 X - 35
Need help id appreciate it
Answer:
x=14
Step-by-step explanation:
If the square from GAI are 6 cm, then the other half of the triangle is also 6 inches long. Because it is not an even sided triangle, all the sides shouldnt be the same size. If you multiply 6 by 2 you get 12. 7 times 6 is 42. 42 divided by 3 is 14. The value of X should be 14.
write the equation of the like that is parallel to the line y=3x+6 and passes through the point (4,7)
Answer:Find the slope of the original line and use the point-slope formula
y
−
y
1
=
m
(
x
−
x
1
)
to find the line parallel to
y
=
3
x
+
6
.
y
=
3
x
−
5
Step-by-step explanation:
What is the perimeter of this polygon?
L2FwcGhvc3RpbmdfcHJvZC9ibG9icy9BRW5CMlVwYkZOdjFTNENGM2w5NTZIbzhybUFJSFlheFNqdmRHMm5BaFpQMUJONnRQcUJobDZYM3AxY29yRFVwWFJWeXc5cU5GQWhDajdDZGN3YUpSYVRmNV8wUzV2LVhSZy54azBYdVdxSDBkeHYxQ0Fs?w=400&h=400
a
24 units
b
22 units
c
28 units
d
26 units
Answer:
I am pretty sure it is
B. 22 units
Step-by-step explanation:
Answer:
24 units.
Count how many boxes make up the outside of the shape. Perimeter is just the distance around the shape.
Let me know of any other questions! :)
Holly is making fruit salad. She bought 3 pounds and 3 ounces of fruit. How many ounces of fruit did she buy? *Needed ASAP
Answer:
Step-by-step explanation:
do 3 x 16 = 48 + 3 is 51
5y + 3y + 5 ≤ ‐2(2y + 4)
Answer:
y≤−13/12
Step-by-step explanation:
Answer:
y ≤ -13/12 or y = (-oo, -13/12]Step-by-step explanation:
5y + 3y + 5 ≤ ‐2(2y + 4)8y + 5 ≤ - 4y - 88y + 4y ≤ -8 - 512y ≤ -13y ≤ -13/12ory = (-oo, -13/12]This makes so much sense now I’m broken
Answer: well my two favorite christmas movies just got confusing and kinda ruined at the same time. LOL. BUT it makes sense also if u think abt it he also he has a dog named max, but jack has one named zero so did he just change his name or find a different dog
Need help will give brainleist
Answer:
41º
Step-by-step explanation:
Because of parallel lines, (2x-5)º=180º-113º, so (2x-5)º=67º.
(2x-5)º=67º2x-5=67º2xº=72ºx=36ºThe angle that says (2x)º will be (2[36])º=72º.
So the other angle will be 180-67-72=41º as the sum of a triangle's interior angles is 180º.
Answer:
41°
Step-by-step explanation:
The angle below (2x-5) is also 113° (which i hope you know why)
Then to find (2x-5)° you would subtract 180 - 113 to get the angle because both those angles would add up to 180° because it is a straight angle which gives you 67°
Then you need to find x by solving the equation 2x - 5 = 67 which would give you x = 36, so you would multiply that by 2 for the angle on the side which would be 72°
Then bc the angles on the inside of the triangle all add up to 180° as well, you would add 72 + 67 = 139, then do 180 - 139 giving you d° as 41°
A snail travels 10 cm in 4 minutes. At this rate, how far will the snail get in 10 minutes?
Answer:
25CM
Step-by-step explanation:
Answer:
25 cm
Step-by-step explanation:
10*2.5 is the method I used.
The editors of a local
newspaper went to lunch to
celebrate birthdays. The
lunch costs $17.8.25 and they
left a 15% tip. What was the
cost of the meal?
Answer:
$111.52
Step-by-step explanation:
You have to divide your total amount by 1.15 and that will give you your answer. To check your work you can add your answer and 15% of your answer together. {111.52+(111.52x0.15)=128.25}
-z=8
Evaluate and solve for the variable
Answer:
z=-8
Step-by-step explanation:
Answer:
isnt there supposed to be more numbers?
Step-by-step explanation:
Help!!!!!!!!!!!!!!!!!!!!!
Answer:
D is the correct answer
Step-by-step explanation:
hope it helps
have a great day
:)
Number 1
In the relation, what is the domain?
I
In the relation, what is the range?
Answer:
Step-by-step explanation:
D(x)= (-1, -1\2, 3/2, 2)
A domain is any X value in an array of ordered pairs
If a data set has mean of 150 and a standard deviation of 25, what is the z-score of an element with a value of 250?
Answer:
Z-score is 4
Step-by-step explanation:
N(150, 25^2)
Use z-score formula (can be found from internet with miu and sigma symbol)
[tex]z = \frac{250 - 150}{25} \\ z = \frac{100}{25} \\ z = 4[/tex]
at one high school, the mean time for running the 100-yard dash is 15.2 seconds with a standard deviation of 0.9 seconds. the times are very closely approximated by a normal curve. find the percent of times that are at least 14.3 seconds
Answer:
The percent of times that are at least 14.3 seconds is approximately 16%.
Step-by-step explanation:
Let X denote the time for running the 100-yard dash.
It is provided that the times are very closely approximated by a normal curve.
So, the random variable X follows a normal distribution with a mean time of 15.2 seconds and with a standard deviation of 0.9 seconds.
Compute the probability of times that are at least 14.3 seconds as follows:
[tex]P(X\geq 14.3)=P(\frac{X-\mu}{\sigma}\geq \frac{14.3-15.2}{0.9})[/tex]
[tex]=P(Z\geq -1)\\\\=1-P(Z<-1)\\\\=P(Z<-1)\\\\=0.15866\\\\\approx 0.159[/tex]
*Use a z-table.
Thus, the percent of times that are at least 14.3 seconds is approximately 16%.
The function f(x) =x^3 +2x has an inverse function g. Find g’(0) and g’(3).
Step-by-step explanation:
follow the steps to get answer
Name the subset(s) of real numbers to which each number belongs. Then order the numbers from least to greatest.
45−−√ , 16/5 , −1
Answer:
I'm assuming 45−−√ is [tex]\sqrt{45}[/tex], and that it belongs to the subset of irrational numbers.
16/5 is a rational number, and -1 is an integer.
All numbers belong to the subset of real numbers.
Step-by-step explanation:
Hope this helped!
Find the commission.
Earning Commission
Sales Commision Rate Commission
$750
9%
?
The commission is $
Answer:
The commission would be $67.50.
Answer:
$67.50
Step-by-step explanation:
commission amount = sale price * commission percentage / 100
A recipe requires \frac{1}{3}
1
3
cup of milk for each \frac{1}{4}
1
4
cup of water. How many cups of water are needed for each cup of milk?
Answer:A
Step-by-step explanation:
A
Deanna Jones opened a video rental store this year with 400 tapes. She plans to buy 150 new tapes each year from now on. Deanna expects to have 1300 tapes available during her fifth year in business. At her current purchasing rate, will she reach her goal? Explain.
A. No, she will have only 1150 tapes.
B. Yes, she will have exactly 1300 tapes.
C. Yes, she will have over 1300 tapes.
HURRY NEED SOON PLEASE
students set up 6 rows of seats for a music concert. they put 6 seats in each row. what is the total number of seats? solve this problem any way you choose
Answer:
36
Step-by-step explanation:
becuase each row has 6 in them and there are 6 rows so 36 is the final answer