Find the equation of an exponential function of the form y = ab^x that passes through the points (3,13.5) and (5,30.375).

Answers

Answer 1

Let's see

y=ab^x

Check coordinates

13.5=ab³-(1)

Find a

a=13.5/b³---(2)

And

30.375=ab⁵

Put value from second one

30.375=13.5b⁵/b³30.375=13.5b²b²=2.25b=1.5

Put in second one

a=13.5/b³a=13.5/1.5³a=13.5÷3.375a=4

So the equation is

y=4(1.5)^x
Answer 2

Answer:

[tex]y=4(1.5)^x[/tex]

Step-by-step explanation:

General form of an exponential function: [tex]y=ab^x[/tex]

where:

a is the y-intercept (or initial value)b is the base (or growth factor)x is the independent variabley is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Given ordered pairs:

(3, 13.5)  and  (5, 30.375)

As the y-values are increasing, the function is increasing, so b > 1

Input the given ordered pairs into the general form of the equation:

[tex]\implies ab^3=13.5[/tex]

[tex]\implies ab^5=30.375[/tex]

To find b, divide the second equation by the first:

[tex]\implies \dfrac{ab^5}{ab^3}=\dfrac{30.375}{13.5}[/tex]

[tex]\implies b^2=2.25[/tex]

[tex]\implies b=\pm \sqrt{2.25}[/tex]

[tex]\implies b= \pm 1.5[/tex]

As the function is increasing, b > 1:

⇒ b = 1.5  only

Substitute the found value of b into one of the equations and solve for a:

[tex]\implies a(1.5)^3=13.5[/tex]

[tex]\implies 3.375a=13.5[/tex]

[tex]\implies a=\dfrac{13.5}{3.375}[/tex]

[tex]\implies a=4[/tex]

Therefore, the final exponential equation is:

[tex]y=4(1.5)^x[/tex]


Related Questions

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER

Answers

Answer:

227

Step-by-step explanation:

Since they give you the hypotenuse length of 290in and they ask you to find the length os the adjacent angle, use the cosine to find side b.

So you do tan38=b/290 then calculate.

The true answer is 226.5728 but they ask you to round.

23) A movie theatre has 900 seats of which 15% are in the balcony. How many seats are NOT in the balcony?
A.
765
B.
90
C.
785
D.
875

Answers

Answer:

A.765 seats are not in the balcony

Step-by-step explanation:

if 15% are in the balcony then 85% are not in the balcony so..

900 * 0.85 = 765

Answer:

765

Step-by-step explanation:

900*.15=135

900-135 = 765

What is the value of x

Answers

Answer:

your answer is 20.

Step-by-step explanation:

x^2+4^2=(2+x)^2

one day a store sells 14 pairs of jeans . The 14 jeans represents 20% of total number of items sold that day. How many items did the store sell in one day

Answers

Answer:

items sold in 1 day = 140

Step-by-step explanation:

14 pairs of jeans = 28 jeans total

the 14 "pair of jeans" repesents 20% of the total = x

28 = 20x/100

2800/20 = x

x = 140

An architect drew the blueprint for a new office building. He used a scale in which 1 inch represents 7.5 feet. The floor of an office in the building will have actual dimensions of 14 feet by 24 feet. What will the dimensions on the blueprint be?
A.
105 inches by 180 inches
B.
21.5 inches by 31.5 inches
C.
6.5 inches by 16.5 inches
D.
1.87 inches by 3.2 inches

Answers

Since we know the scale factor of 1 inch represents 7.5 feet, we can plug in the dimensions for the scale on which the architect drew.

For 14 feet, we can multiply 14 by 1 inch/7.5 feet to get a product of 1.87 inches. Then, we can do the exact same thing with the other width of the floor, which is 24. 24 × 1/7.5 = 3.2

The final dimensions of the blueprint will be D, 1.87 inches by 3.2 inches.

Factor the binomial.
4z2 − 25
4z2 − 25 =

Answers

[tex]4z^2-25\\\\=(2z)^2-5^2\\\\=(2z+5)(2z-5)[/tex]

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER

Answers

Answer:

e

is congruent with x f is congruent with x and g is congruent with y Step-by-step explanation:

angle E = angle X

angle F = angle Y

angle G = angle Z

hope it helps...!!!

Efficiently solve

A. 30x70+37x70
B. 335x11-135x11
C. 223x87-123x87
D. 3.2x120+16.8x120
E. 555x0.08-545x0.08
F. 3.45x17-1.45x17
G. 0.7x0.7x85

Thanks so Much if you Help me!

Answers

Answer:

Step-by-step explanation:

A. 2100+2590= 4,690

B. 3685-1485=2,200

C. 19,401-10,701= 8,700

D. 384+2,016=2,400

E. 44.4-43.6=0.8

F. 58.65-24.65=34

G. 41.65

A. 2100+2590=4,690
B. 3685-1485=2,200
C. 19,401-10,701=8,700
D.384+2,016=2,400
E.44.4-43.6=0.8
F.58.65-24.65=34
G.41.65

urgent help please! ^^ <3

Answers

Answer:

Lower quartile = 6

Median = 8

Upper quartile = 9

Step-by-step explanation:

If you take away a number from each end of the number set one by one, you will end up with 7 and 9 in the middle. To find the median between two numbers, add them together then divide them by 2.

7 + 9 = 16

16 ÷ 2 = 8

_________________

To find the lower and upper quartiles, split the number set into two where the median is, then, find the median of those two sections.

Lower quartile: 4, 5, 6, 6, 7

Median = 6

-

Upper quartile: 9, 9, 9, 9, 9

Median = 9

So, the median of the whole set is 8, the lower quartile is 6, and the upper quartile is 9.

hope this helps!

rewrite each equation in exponential form. log 100=2

Answers

Answer:

10x^{2} = 100

Step-by-step explanation:

Use the definition of a logarithm, logb(x)=y ⟹ by=x, to convert from the logarithmic form to the exponential form.

Hopefully this helps you

- Matthew

What is the probability of landing on an odd number and then landing on a number greater than 7?

Answers

Answer:

72%

Step-by-step explanation:

a
It takes 15 minutes to drain a pool containing
45 gallons of water. If a similar pool takes 35
minutes to drain at the same rate, how many
gallons of water are in the similar pool?

Answers

Answer:

there is 92.25

Step-by-step explanation:

15x2=30

then you have to find out 5% out of 45 because you need to get 35 not 30.

Sophia invest money in an account paying simple interest. She invest 100$ and no money is added or removed from the investment. After one year, she has 108. What is the simple percent interest per year ?

Answers

Answer:

8%

Step-by-step explanation:

She earned 8 dollars on a 100 dollar investment

8/100 = 8%

The answer is  8%

What Is Simple Interest?

Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.

Given here: Principal as $100 and return as $108 and t=1

Thus 8=100×1×r /100

r=8%

Hence, The rate of interest is 8%

Learn more about simple interest here:

https://brainly.com/question/25845758

#SPJ2

what is the product of mixed number 2 x 2 7/8?

Answers

Answer:

[tex]5\frac{3}{4}[/tex]

----------------------------------------------------------------------------------------------------------

Since we have to convert mixed numbers to fractions, [tex]2\frac{7}{8}[/tex] becomes [tex]\frac{23}{8}[/tex]

And for whole number, add a 1 as the denominator.

[tex]\frac{2}{1}[/tex]

Now, the equation becomes...

[tex]\frac{2~*~23}{1~*~8}[/tex]

[tex]2 * 23 = 46[/tex]

[tex]1 * 8 = 8[/tex]

Convert these two numbers to a fraction.

[tex]46~and~8~-- > ~\frac{46}{8}[/tex]

Simplify 46 over 8 and make it a mixed number.

[tex]\frac{46}{8} -- > 5\frac{3}{4}[/tex]

why is the denominator 4? we had to simplify 8 using its GCF along with 46

the GCF is 2, so simplify using 2. to simplify, divide the number by its GCF.

[tex]\frac{46}{2} = 23\\\\\frac{8}{2} = 4[/tex]

now you have [tex]\frac{23}{4}[/tex]

and that, in mixed number, translates to [tex]5\frac{3}{4}[/tex]

________________________________________________________

Questions?

Ask in comments.

3) Solve the equation for x.
10(4x + 4) = 400
A) 2
B) 4
C) 9
D) 18

Answers

Answer:

C) 9

Step-by-step explanation:

10(4x + 4) = 400

40x + 40 = 400

40x = 360

x = 9

Answer:

First factor out the expression

(10•4x)+(10•4)=400

40x+40=400

Then solve

40x+40=400

-40 = -40

40x=360

------ ------

40 40

x=9

C) 9

☆anvipatel77☆

•Expert•

Brainly Community Contributor

Ezekiel manages a clothing store. In May, sales were $129,800. In June, sales were $131,975. What was the rate of change?

Answers

The rate of change of the sles of the clothing store that Ezekiel manages from May to June is $2,175

What is the rate of change?

Subtraction is the mathematical operation that involves determining the difference between two or more numbers.

Rate of change = sales in June - sales in May

$131,975 -  $129,800 = $2,175

To learn more about subtraction, please check: https://brainly.com/question/854115

#SPJ1

If a marble is randomly chosen from a bag thay contains exactly 8 red marbles, 6 blue marbles, and 6 white marbles, what is the probability that the marble will not be white?

Answers

Answer: 7/10

Step-by-step explanation:

The probability of an event can be calculated as:

[tex]P(E)=\frac{n(F)}{n(T)}[/tex]

Where n(F) is favorable outcomes and n(T) is total possible outcomes.

The total number of marbles can be obtained as,

8 + 6 + 6 = 20

The probability of marble being white can be calculated as,

[tex]P(W)=\underline{\frac{6}{20}}[/tex]

Now, the probability of the marble not being white can be evaluated as,

[tex]\begin{aligned}P^{\prime}(W) &=1-\frac{6}{20} \\&=\frac{20-6}{20} \\&=\frac{14}{20} \\&=\frac{7}{10}\end{aligned}[/tex]

Therefore, the probability of the marble not being white is 7/10

PLS HELP ME I NEED AN A I GIVE 50 POINTS

Answers

Answer:

The one on the left shows a proportional relationship between x and y.

Step-by-step explanation:

equation your going to use = y ÷ x or y/x (both mean divide)

2÷4 = 0.5

5÷10 = 0.5

6÷12= 0.5

All have the same answers so that makes it a proportional relationship.

In the equation 4x4=16, 4 is a:

Answers

Answer:

4 is a factor

Step-by-step explanation:

thats what a number being multiplied is called

Please see attached photo for problem from my homework set.

Answers

Answer: (x - 1)(x - 23)

Step-by-step explanation:

    First, we can factor the x² part:

(x)(x)

    Next, we will look at the -24x and +23

-> We need two numbers that multiply to 23 and add to -24

-> 23 is a prime number, so we will use 1 and 23

    For -24, 1 and 23 must be added together. Since a negative times a negative is a positive, and a negative plus a negative is a positive, we will turn them into -1 and -23.

    This gives us a final answer of:

(x - 1)(x - 23)

Answer: (x - 1)(x - 23)

Step-by-step explanation:

attached the picture below of the working...

hope that helps...

will pay the first one that answers this question

Answers

Answer:

a. I

b. II

c. IV

Rewrite as a single logarithm: 3 log b x+4 log b y​

Answers

Answer:

log_b x^3y^4

Step-by-step explanation:

see image

A standard number cube is tossed. Find P( greater than 3 or odd).

Answers

Answer:

Step-by-step explanation:

P= probablity

P (>3  or odd)  

assuming this std.  number cube is 1 to 6, then,

greater than 3 is 50%

so  we've accounted for   1, 3, 4, 5, 6 on the dice what's left  2  :D

so P( >3 or odd) = 5/6  or  83.3333333333333%

Answergrater than 3

Step-by-step explanation:

lisa rides her bike 15.25 miles to and from her job each week. How many miles does she bike in all to and from work in 19.5 weeks?

Answers

Answer:

297.375 miles

Step-by-step explanation:

Since lisa rides 15.25 miles in 1 week and we are looking for how many miles she rides in 19.5 weeks, we must multiple 15.25 miles by 19.5 because she rides 15.25 miles, 19.5 times.

15.25*19.5=297.375

Find the surface area of the cylinder. Round your answer to the nearest tenth.

Answers

yo wheres the cylinder

Which is the correct option, I’m very confused by this question?

sin2x=

Answers

Answer:

The answer is definitely Option A

A person has a bag containing quarters and dimes. There are a total of 61 coins in the bag, and the total value of the coins is $10.45.

Answers

Answer:

Q+D = 65, multiply both sides by 2525Q + 25D = 162525Q + 10D = 950  subtract to get            15D = 675               D = 675/15 = 135/3 = 45 dimes               Q = 65-45 = 20 quarters25(20) + 10(45) = 500+450 = 950

Help me with this math problem please

Answers

Answer:

First Option (-4,-3)

Step-by-step explanation:

x+2y=-10

-y=3x+15

-4+2(-3)=-10
-10=-10

-3=3(-4)+15
-3=-3

Line /has a what slope.
1.negative
2.0
3.positive
4.undefined

Answers

positive because it’s going upwards towards the right.

. If you have a cube measuring 1 unit on
each side, how many of those cubes
would fit into a space 5 units by 5 units
by 5 units?

Answers

Answer:

cubes = (5)(5)(5)

number of cubes =125

to fit

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