Write an exponential function in the form y=ab^x that goes through points (0,6) and (5, 6144)

Answers

Answer 1

Given:

An exponential function goes through points (0,6) and (5, 6144).

To find:

The exponential function.

Solution:

The general form of an exponential function is

[tex]y=ab^x[/tex]          ...(i)

It goes through points (0,6) and (5, 6144). It means the equation must be satisfied by these two points.

Putting x=0 and y=6, we get

[tex]6=ab^0[/tex]

[tex]6=a[/tex]

Putting a=6, x=5 and y=6144, we get

[tex]6144=6b^5[/tex]

[tex]\dfrac{6144}{6}=b^5[/tex]

[tex]1024=b^5[/tex]

Taking 5th root on both sides, we get

[tex]\sqrt[5]{1024}=b[/tex]

[tex]4=b[/tex]

Putting a=6 and b=4, we get

[tex]y=6(4)^x[/tex]

Therefore, the required exponential function is [tex]y=6(4)^x[/tex].


Related Questions

PLEASE HELP
I HAVE TO FINISH IN 5 MINS

Answers

Step-by-step explanation:

the answer is

Remove 8 anchors

Which is the measure of < B?

Answers

a (42 degrees) bc the angles are across from each other so they’re equal

Ralph hit 20 balls in the batting cage last week
This week he hit 15 balls
What is the percentage decrease

Answers

Answer:

Step-by-step explanation:

A water tank has a square base of area 5 square meters. Initially the tank contains 70 cubic meters. Water leaves the tank, starting at t=0, at the rate of 2 + 4 t cubic meters per hour. Here t is the time in hours. What is the depth of water remaining in the tank after 3 hours

Answers

Answer:

[tex]9.2\ \text{m}[/tex]

Step-by-step explanation:

[tex]b[/tex] = Surface area of base = 5 square meters

Volume of water in tank = 70 cubic meters

The rate at which the volume is reducing is

[tex]\dfrac{dV}{dt}=2+4t\\\Rightarrow dV=2+4tdt[/tex]

Integrating from [tex]t=0[/tex] to [tex]t=3[/tex]

[tex]V=\int^3_0(2+4t)dt\\\Rightarrow V=2t+2t^2|_0^3\\\Rightarrow V=2\times 3+2\times 3^2-0\\\Rightarrow V=24[/tex]

Volume of water remaining in the tank is [tex]70-24=46\ \text{m}^3[/tex]

Suface area of base [tex]\times[/tex] depth = Volume

[tex]5\times d=46\\\Rightarrow d=\dfrac{46}{5}\\\Rightarrow d=9.2\ \text{m}[/tex]

The depth of the water remaining in the tank is [tex]9.2\ \text{m}[/tex].

What is the range of possible sizes for side x?

Answers

Answer:

Your answer is

1/2 <x<8

as per triangular rules

Hope that this is helpful. Tap the crown button, Like & Follow me

ork and check your ansu
x + 5 - 4x = 8

Answers

Answer:

x = -1

Step-by-step explanation:

x+5-4x=8

-5       -5

x-4x=3

-3x=3

/-3    /-3

x=-1

ANSWER NEEDED QUICKLY, RIGHT ANSWER GETS BRIANLIEST!

Angel gave the store clerk $50 to buy 4 T-shirts. The store clerk gave her
$18.16 in change. Each T-shirt cost the same aount.
What is the cost in dollars and cents for each T-shirt?

Answers

Answer:

7.96

Step-by-step explanation:

50-18.16=31.84

31.84 divided by 4 = 7.96

Answer:

Each T - shirt costs $7.96

Step-by-step explanation:

4x + 18.16 = 50

subtract 18.16 from both sides.

4x = 31.84

divide both sides by 4

x = 7.96

What is the solution to the equation? 8/2.1 = 15.3 someone plz help

Answers

Answer:

5.8

Step-by-step explanation:


After a 10% decrease the cost of a new cooker is £ 198
Work out the original price of the cooker.

Answers

Answer:

£217.80

Step-by-step explanation:

198 increase 10% =

198 × (1 + 10%) = 198 × (1 + 0.1) = 217.8

Hayden wanted to investigate whether there was a difference in the time spent in the checkout line between two grocery stores. She went to Safeway on a Tuesday morning and recorded the time, in minutes, it took 30 customers to go through a checkout line. Then she went to Whole Foods on Tuesday afternoon and recorded the time it took 30 customers to go through a checkout line. Hayden calculated the mean number of minutes for the customers in each line. She intends to conduct a two-sample t-test for a difference in means between the two stores. Have all conditions for inference been met

Answers

Answer:

No.  The data in this study were not based on a random method.  This is a key requirement for an inference to be made from the two-sample t-test.

Step-by-step explanation:

1. Hayden can use the two-sample t-test (also known as the independent samples t-test)to find out if there was a difference in the time spent in the checkout time between two grocery stores and to conclude whether the difference in the average checkout time between the two stores is really significant or if the difference is due to a random chance.  There are three conditions to be met when using the two-sample t-test.

2. The first condition is that the sampling method must be random.  This requirement was not met in this study.  Each customer from each store should have an equal chance of being selected for the study.  This was not achieved.

3. The distributions of the sample data are approximately normal.  This is achieved with a large sample size of 30 customers selected for each study.

4. The last but not the least condition is the independence of the sample data.  Sample data here is independent for both samples.

what is the graetest commom factor for 6 and 36

Answers

Answer:

The greatest common factor of 6 and 36 is

6

Hope it will help :)

Answer:

6

Step-by-step explanation:

Which digit(s) make the solution of the equations the whole number ?
5x-347=2,16...
Don’t find X

Answers

Answer:

SOMEONE HURRY AND FIND THE ANSWER

Step-by-step explanation:

5x=216+347
5x=563
X=563
5
X = 563 over 5 is the answer
Do it fouse to be a common there or not I’m loss on that part next time make it clear please

0.5(5x - 2.2 )
Expand the expression

Answers

Answer:

2.5x - 1.1

Step-by-step explanation:

0.5 x 5x = 2.5x

0.5 x 2.2 = 1.1

I hope this helps! :)

Jasmine evaluated the expression 3x+2 when x=5.

3x+2

35+2

37
Explain Jasmine’s mistake.

Answers

Answer:

when x = 5

then the value of. (3x+2)

(3*5) + 2

15 + 2

=. 17

her mistake was that she doesn't multiplied 5 and 3

Which equation represents a line which is perpendicular to the line y = 23 – 4?

Answers

Answer:

y=19

Step-by-step explanation:

EASY: order from largest to smallest size

Answers

Answer:

Decending

Step-by-step explanation:

Answer:

1,2,3

Step-by-step explanation:

Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of 10%, test the hypothesis that the three formulas produce the same mean weight gain.
Linda's rats Tuan's rats Javier's rats
43.5 47.0 51.2
39.4 40.5 40.9
41.3 38.9 37.9
46.0 46.3 45.0
38.2 44.2 48.6
Determine whether or not the variance in weight gain is statistically the same among Javier’s and Linda’s rats. Test at a significance level of 10%.

Answers

Answer:

The variance in weight is statistically the same among Javier's and Linda's rats

The null hypothesis will be accepted because the P-value (0.53 ) > ∝ ( level of significance )

Step-by-step explanation:

considering the null hypothesis that there is no difference between the weights of the rats, we will test the weight gain of the rats at 10% significance level with the use of Ti-83 calculator

The results from the One- way ANOVA  ( Numerator )

with the use of Ti-83 calculator

F = .66853

p = .53054

Factor

df = 2  ( degree of freedom )

SS = 23.212

MS = 11.606

Results from  One-way Anova ( denominator )

Ms = 11.606

Error

df = 12 ( degree of freedom )

SS = 208.324

MS = 17.3603

Sxp = 4.16657

where : test statistic = 0.6685

             p-value = 0.53

             level of significance ( ∝ ) = 0.10

The null hypothesis will be accepted because the P-value (0.53 ) > ∝

where Null hypothesis H0 = ∪1 = ∪2 = ∪3

hence The variance in weight is statistically the same among Javier's and Linda's rats

Shade the number line to show 3/5 x 5/8

Answers

Answer:

15/40 = 3/8

Step-by-step explanation:

numerator x numerator & denominaror x denominaror

To shade this on a number line, we can find the point that corresponds to 0.375 and shade it.

What is a number line?

It is the representation of numbers in real order.

The difference between the consecutive numbers in a number line is always positive.

We have,

To shade the number line to show 3/5 x 5/8, we can first convert the fractions to decimals:

So,

3/5 = 0.6

5/8 = 0.625

Next,

We can multiply these decimals together to find the product:

= 0.6 x 0.625

= 0.375

To shade this on a number line, we can find the point that corresponds to 0.375 and shade it.

If the number line extends from 0 to 1, with tick marks every 0.1, we can count over 3.75 tick marks from 0 and shade the point that corresponds to that location.

The shaded point should fall between 0.3 and 0.4 on the number line.

Thus,

To shade this on a number line, we can find the point that corresponds to 0.375 and shade it.

Learn more about number line here:

https://brainly.com/question/13425491

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Negative numbers: addition and subtraction: Qui
Which of the following expressions are
4 8 4 9
equivalent to
+- ?
7 9 7 8
Choose 2 answers:
4
8
-
+
9
+
TIN
8
4
+15
1
-
+
+
+
8
4
8
+
+
+
7.
8.
0

Answers

Answer:

+15 and 9

Step-by-step explanation:

i hvae this for hw can anyone help me out rq?

Answers

Answer:

0 1 and 5

Step-by-step explanation:

Not 6 because its an open dot which means that 6 is not included

I hope this helps?

Dependent events can best be described as
two or more events that have the same probabilities.
two or more events that do not have the same probabilities.
a group of events whose later outcomes are not affected by previous outcomes.
a group of events whose later outcomes are affected by previous outcomes.

Answers

Answer:

Sonya watched

1

3

of a movie in the morning, and she watched some more at night. By the end of the day, she still had

1

4

of the movie left to watch. How much of the movie did Sonya watch at night?

Step-by-step explanation:

SORRY WRONG

Dependent event is,

D) a group of events whose later outcomes are affected by previous outcomes.

What is mean by Probability?

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We know that;

The two events Event A and event B are said to be dependent if the occurrence of one outcome affects the occurrence of the other outcome.

Since, If we have a bag containing 5 blue marbles, 2 red marbles and 3 green marbles then if we draw first marble and then draw second without replacement.

Then, the event of drawing a blue marble first and then a green marble are dependent events.

Hence, Dependent event is,

a group of events whose later outcomes are affected by previous outcomes.

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ5

what is the standard form for 7x + 3x^2

Answers

Answer:

10x^3

Step-by-step explanation:

7+3=10

10x^2

easy

Equivalent Ratios: 300:800 = 30:

Answers

Answer:

30:80

Step-by-step explanation:

Because 300 divided by ten is 30 so 800 divided by ten is 80 :)

Pls help meeeeeeeeeeeee

Answers

Answer:

4 Hours and 25 Minutes to Seconds is - 15900

Step-by-step explanation:

Suppose you and a friend form a band. You want to record a demo. Sony Studios rents for $150 plus $20 an hour. Capitol Studios rents for $200 plus $15 an hour. Use a system of equations to help you to determine when the studios charge the same amount.

at what number of hours do the studios charge the same amount?

Answers

Answer:

200 < 225 + 80x < 550

The 200 is the amount the Jenna currently have.

225 + 80x is the amount that Jenna has to pay given x number of hours.

550 is the sum of Jenna's 200 and additional 350 she can get by selling pre-ordered Cds. This is the maximum amount she can pay for the studio rental and sound technicians.

Step-by-step explanation:

225 + 80x < 550

80x < 550 -225

80x < 325

80x / 80 < 325/80

x < 4.06 or 4 hours

225 + 80x → 225 + 80(4) = 225 + 320 = 545

The number of hours for the sound technician will range from 1 hour to 4 hours.

Assuming they will use 6 hours.

225 + 80(6) = 225 + 480 = 705

705 - 550 = 155

Jenna has to raise an additional $155 to pay off the studio rent and 6 hours of sound technicians.

this might be wrong but, i hope it helps

Answer:

Step-by-step explanation:         times the hour by four on each and get 60 then it would be an equal pay for the hours.

Pls help me answer the question attached

Answers

Mai - 6 and 3/4 is 6.75 miles
Noah - 4 and 1/2 is 4.5 miles

To find out how many times the length of Noah’s bike ride was Mai’s, you would divide so

6.75/ 4.5 = 1.5

Therefore the answer would be
b) 3/2 times as far

Answer:

A.

Step-by-step explanation:

(2/3)*6.75=4.5

Helps pls help pls thank you so much

Answers

Answer:

Increases, same, increases, decreases

Step-by-step explanation:

I mean just look at the graph

Write the fraction as a product of a whole number and a until fractions 7/8

Answers

Answer: 8/9 cause we sub

Step-by-step explanation:

Complete this for me

Answers

Answer:

Step-by-step explanation:

1 Kg of carrot = 40 p

1 1/2 Kg of carrot = 40 * [tex]\frac{3}{2}[/tex]  = 20 * 3 = 60 p  = £ 0.60

1 kg of potato = 52 p

3 kg of potato = 52 *3 = 156 p =  £1.56

1 box of tea bags = 90 p

Number of boxes for  £1.80 = 1.80 ÷ 0.90  = 2 boxes

4 packs of yogurt =  £4.80

1 pack of yogurt   = 4.80 ÷ 4 =  £1.20

Total = 0.60 + 1.56 + 1.80 +4.80 =  £ 8.76

A basketball hoop is 15 feet tall. The angle of elevation to the hoop from Jasmine is 75 degrees. How far away is Jasmine from the base of the basketball hoop (horizontal distance)? Round to the nearest hundredth.

Answers

Answer:

75 Feet

Step-by-step explanation:

123

jk

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