What kind of growth model (pattern) is shown in the table? x y 1 5 2 25 3 125 4 625 5 3,125 a. square root b. linear c. exponential d. quadratic

QUESTION POSTED AT 19/02/2020 - 03:44 PM

Answered by admin AT 19/02/2020 - 03:44 PM

Answer:

Option C is correct.

The kind of growth model is shown in the table is exponential

Step-by-step explanation:

Exponential growth function is in the form of :  y = ab^x  ......[1];   where a is the initial value and b> 0.

Consider any two point from the table:

(1 , 5) and ( 2 , 25)

Substitute these in the equation [1] we get;

5 = ab^1         ......[2]

25 = ab^2      ......[3]

Divide equation [3] by [2] we have;

\frac{25}{5} = \frac{ab^2}{ab}

Simplify:

5 = b

Now substitute this value in equation [2] we get;

5 = a \times 5

Divide both sides by 5 we get;

\frac{5}{5} = \frac{5a}{5}

Simplify:

1=a or a = 1

Therefore, the table shown the  exponential growth function is, y = 5^x

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Related questions

A random sample of 125 students is chosen from a population of 4,000 students. If the mean IQ in the sample is 100 with a standard deviation of 8, what is the 98% confidence interval for the students' mean IQ score?

Answer: 98.33 - 101.67


Step-by-step explanation:

The given Sample mean n= 100  

Standard deviation\sigma=8

Mean IQ in the sample \bar{x}=125

Standard error of mean = \frac{\sigma}{\sqrt{\bar{x}}}

Standard error of mean = \frac{8}{\sqrt{125}}

Thus, standard error =\frac{8}{11.180}

Standard error of mean (SE)= 0.7155  

We know that  z - score for 98% confidence interval is 2.33 .

Now, 98% confidence interval will be

n-z(SE) and n+z(SE)

=100-(0.7155)(2.33)\ and\ 100+(0.7155)(2.33)  

=100-1.66726\ and\ 100+1.66726

=98.33274\ and\ 101.667

Hence, the 98% confidence interval for the students' mean IQ score will be 98.33 - 101.67



ANSWERED AT 31/03/2020 - 10:47 AM


QUESTION POSTED AT 31/03/2020 - 10:47 AM

What's the square root of 100

The square root would be ten because  10^2 power equals 100

ANSWERED AT 31/03/2020 - 10:42 AM


QUESTION POSTED AT 31/03/2020 - 10:42 AM

Find the area of the shaded portion of the diagram (use 3.14 for p).A)220.16 square yardsB)6.88 square yardsC)55.04 square yardsD)13.76 square yards

Get the area of the circle. Use this formula: 
Area =  \pi * radius^2

We know the radius is 4 yards.

Area = 3.14 * 4^2
Area = 3.14 * 16
Area = 50.24

Now for the square. Double the radius to get the diameter to get the length of the side.

4 * 2 = 8

Formula for finding the area of a square is
Area = side^2

Area = 8^2
Area = 64

And because we only want to shaded portion, we will subtract the area of the circle from the square.

64 - 50.24 = 13.76

So, 
D) 13.76 square yards is the answer to this question.

ANSWERED AT 31/03/2020 - 10:38 AM


QUESTION POSTED AT 31/03/2020 - 10:38 AM

A regular hexagon with side length 4 has the same area as a square. What is the length of the side of the square?

The length of the side of the square would be 6.4

ANSWERED AT 30/03/2020 - 01:31 AM


QUESTION POSTED AT 30/03/2020 - 01:31 AM

A population of 1,000 squirrels lives on a rectangle-shaped farm plot that is 25 feet long by 10 feet wide what is the population density

First, find the area of the plot:
25*10=250

1000/250 is 4

the population density is 4 squirrels per square foot.

ANSWERED AT 30/03/2020 - 01:30 AM


QUESTION POSTED AT 30/03/2020 - 01:30 AM

Graph this linear function using slope intercept: y=2x+9

I really dont know lol.
                

ANSWERED AT 29/03/2020 - 11:47 PM


QUESTION POSTED AT 29/03/2020 - 11:47 PM

An angle measures 125 degree. Through what fraction of a circle does the angle turn?

Well a circle is 360 degrees and the angle turns 125 of that. a fraction can be considered a ratio of a part of the whole vs the whole and can be written as:
part/whole

So the part is 125 and the whole is 360 so
125/360

This can be reduced by 5
25/72

That is your answer

ANSWERED AT 29/03/2020 - 06:32 PM


QUESTION POSTED AT 29/03/2020 - 06:32 PM

Jonathan and Sarah purchased a beach house for $10,000,000. The home appreciates at a rate of 3% per year. The appreciation of the house is shown in the graph. The home is currently worth about $13,000,000. Jonathan and Sarah have owned the home for about ______ years. how many years

Current worth = 10,000,000 * (1.03)^years
We must determine the years when current worth = 13,000,000
13,000,000 / 10,000,000 = 1.03^years
1.3 = 1.03^years
Taking logs of both sides:
log (1.3) = years*log(1.03)
log(1.3) / log(1.03) = years
0.11394335231 / 0.012837224705 = years
years = 8.8760113598
Roughly about 8.9 years


ANSWERED AT 29/03/2020 - 06:29 PM


QUESTION POSTED AT 29/03/2020 - 06:29 PM

If there is a crossword that has three squares that need to be filled, how many possible three letter arrangements are there (assuming they do not have to make a real word)? A.26! B.26!/3! C.23! D.26!/23

26 possible letters
assuming you can repeat them
26*26*26
no listed
ok, lets assume that you can't repeat them
that is 26 times 25 times 24 (because you used 1 each time)
that is 26!/23! (because 26*25*24*23!=26!)

answer is D (only if there is a factorial sign after the 23)

ANSWERED AT 29/03/2020 - 06:27 PM


QUESTION POSTED AT 29/03/2020 - 06:27 PM

True or false? The first distribution shown below has a smaller mean than does the second.

The awnser is  It is true

ANSWERED AT 29/03/2020 - 06:25 PM


QUESTION POSTED AT 29/03/2020 - 06:25 PM

Which type of data is BEST described by a continuous model? A) points scored B) pages in a book C) children in a family D) temperature of an engine

The meaning of term continuous is that there should be no breaking.

In terms of mathematics , a function is said to be continuous function if there are no gaps when you plot the curve on coordinate axis.

In option 1, points scored is an incomplete statement.

Option 2, pages in a book is an example of constant function if you count pages between two pages. But it is a continuous function if page numbers are counted.

Option 3, children in a family is not a continuous function because there are gap in birth of two children.

Option 4, Temperature of an engine varies if engine is moving, otherwise remains constant.

Option (B), pages in a book is a type of data which is BEST described by a continuous model.    

ANSWERED AT 29/03/2020 - 06:24 PM


QUESTION POSTED AT 29/03/2020 - 06:24 PM

The picture shows the growth of your two bean plants how much taller has plant A grown then plant B

2/3 -1/4 = 8/12-3/12 so the final answer is 5/12

ANSWERED AT 29/03/2020 - 06:21 PM


QUESTION POSTED AT 29/03/2020 - 06:21 PM

The height in feet of the projectile seconds after lunch is modeled by the equation h=32t - 16t2 how long after launch does the projectile return to the ground

When h=0 is when it returns to the ground
solve

0=32t-16t^2
factor
0=16t(2-t)
set equal to zero

0=16t
0=t

0=2-t
t=2

at t=0 and 2
it returns after 2 seconds

ANSWERED AT 29/03/2020 - 06:19 PM


QUESTION POSTED AT 29/03/2020 - 06:19 PM

100,000 using exponential notation

100,000 in exponential notation is 10 to the fifth power because if you count how many zero are in 100,000 is 5 and 10 is your base number. So 10 to the fifth power is the correct answer. Hope this helped ( :

ANSWERED AT 29/03/2020 - 06:18 PM


QUESTION POSTED AT 29/03/2020 - 06:18 PM

Mario claims that a Rhombus is sometimes a square, but a square is always a rhombus. Is he correct? Explain your answer

No, I know this because a square is not ever a rhombus, a rhombus has acute angels and squares don't.

ANSWERED AT 29/03/2020 - 04:32 PM


QUESTION POSTED AT 29/03/2020 - 04:32 PM

Write the equation for this table and if you can explain(not required)

I need help with the same stuff

ANSWERED AT 28/03/2020 - 12:57 PM


QUESTION POSTED AT 28/03/2020 - 12:57 PM

How do you graph the quadratic function 8(x-6)^2

8 translation: narrow or compress graph by a scale factor of 8
-6 translation: shift graph 6 points right

ANSWERED AT 28/03/2020 - 12:49 PM


QUESTION POSTED AT 28/03/2020 - 12:49 PM

Will’s boss has asked him to compile the credit scores of everyone in his department. The data that Will collected is shown in the table below. What is the mode of the credit scores in Will’s department?634 667 644 892 627 821 857 703 654

Answer:

Mode does not exist

Step-by-step explanation:

Mode of any data set is the data with the highest frequency(i.e. that term which is repeated most in the data set)

Here, credit scores in Will's office are:

634 667 644 892 627 821 857 703 654

No term is repeated hence, the mode does not exist

ANSWERED AT 28/03/2020 - 12:48 PM


QUESTION POSTED AT 28/03/2020 - 12:48 PM

What is the area of triangle DEF? Round to the nearest tenth of a square unit. 10.3 square units 18.0 square units 20.0 square units 20.6 square units

Since we are given 2 sides and 2 angles, we can use the Side Angle Side (SAS) method. The area of a triangle is given by the formula:
Area = absinC/2; where a and b are adjacent sides and C is the angle between a and b.

Area = 5*8*sin31°/2 = 10.3 square units.

ANSWERED AT 28/03/2020 - 12:34 PM


QUESTION POSTED AT 28/03/2020 - 12:34 PM

The first three terms of a geometric sequence are shown below. What is the eighth term of the sequence? A. -128x^8-384x^7 B. 128x^8+384x^7 C. 256x^9+768x^8 D. -256x^9-768x^8

Answer:

Option A is correct.

Step-by-step explanation:

Given:

First term, a = x + 3

second term = -2x² - 6x

Third term = 4x³ + 12x²

Common ratio, r = \frac{-2x^2-6x}{x+3}=\frac{-2x(x+3)}{x+3}=-2x

nth term of GP is gievn by, a_n=ar^{n-1}

So, Eight term = a_8=(x+3)(-2x)^{8-1}=(x+3)(-2x)^{7}=-128x^8-384x^7

Therefore, Option A is correct.

ANSWERED AT 28/03/2020 - 12:31 PM


QUESTION POSTED AT 28/03/2020 - 12:31 PM

Frank wants to put fencing around the border of his rectangular lawn shown. He needs 16 feet of fencing. What is the length of the lawn?

There are manny answers to this
6ft, 6ft, 2ft, 2ft
5ft, 5ft, 3ft, 3ft
7ft, 7ft, 1ft, 1ft
 

ANSWERED AT 28/03/2020 - 12:29 PM


QUESTION POSTED AT 28/03/2020 - 12:29 PM

Express six cups 25 quarts as a fraction in simplest form A. 6/5 B. 3/5 C. 3/10 D. 6/20

D because  6/20  is correct  and the three wrong super wrong hope it helps

ANSWERED AT 28/03/2020 - 12:28 PM


QUESTION POSTED AT 28/03/2020 - 12:28 PM