An exponential function f(x)
= ab" passes through the points (0, 12000) and (2, 3000). What are the values of a and b ?

Answers

Answer 1

Given:

An exponential function [tex]f(x)=ab^x[/tex] passes through the points (0, 12000) and (2, 3000).

To find:

The values of a and b.

Solution:

We have,

[tex]f(x)=ab^x[/tex]      ...(i)

It passes through the point (0,12000). Putting x=0 and f(x)=12000 in (i), we get

[tex]12000=ab^0[/tex]

[tex]12000=a(1)[/tex]

[tex]12000=a[/tex]

Given function passes through the point (2,3000). Putting x=2, a=12000 and f(x)=3000 in (i), we get

[tex]3000=12000b^2[/tex]

[tex]\dfrac{3000}{12000}=b^2[/tex]

[tex]\dfrac{1}{4}=b^2[/tex]

Taking square root on both sides.

[tex]\pm \dfrac{1}{2}=b[/tex]

For an exponential function b cannot be negative. So, [tex]b=\dfrac{1}{2}[/tex].

Therefore, the value of a is 12000 and the value of b is [tex]\dfrac{1}{2}[/tex].


Related Questions

Darron bought a new PS5. He made a down payment of $300, and he will pay $50 each month until the phone is paid off. Which equation represents the relationship between x, the number of monthly payments Darron has made, and y, the total amount he has paid?

A. y= 50x + 300

B. y= -50x + 300

C. x= 50y + 300

D. y= 50x – 300

Answers

D is the current awnser

Answer:

C

Step-by-step explanation:

 tell me how to answer this please I WILL MARK BRAINLIEST

Answers

Answer:

It equals 3

Step-by-step explanation:

To solve this it is basically like a normal problem you would just take out the X in it and divide 7 by 21 which leaves you with 3.

What is the minimum value of the function g (2) = x2 - 6x – 12?
-21
3+ V21
3
3-21

Answers

Answer:

g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12? g (2) = x2 - 6x – 12?

Step-by-step explanation:

Answer:

minimum value is -21;  ordered pair of min value is (3, -21)

Step-by-step explanation:

graph the function and find the lowest point on the curve

In which family of functions can students calculate an average rate of
change? *

Answers

non-linear functions

Average Rate of Change is used primarily with non-linear functions, since all linear functions have a constant rate of change.

Help with his plz ASAP!!

Answers

Answer:

what do you need help on?

X^2+3x+4=(x+a)^2+b what is A and B equal please help me

Answers

Answer:

a = 1.5, b = 1.75

Step-by-step explanation:

Expand the right side using FOIL, then compare the coefficients of like terms with the expression on the left side.

(x + a)² + b

= x² + 2ax + a² + b , then compare to

x² + 3x + 4

Comparing the coefficients of the x- terms

2a = 3 ( divide both sides by 2 )

a = 1.5

Comparing the constant terms

a² + b = 4

1.5² + b = 4

2.25 + b = 4 ( subtract 2.25 from both sides )

b = 1.75

Help please due now!!

Answers

Answer:

60

Step-by-step explanation:

Answer:

Step-by-step explanation:

a = 2 ; b = 4

4a + 2b² - 2(a -3b) = 4*2 + 2(4)² - 2 (2 - 3*4)

                             = 4*2 + 2*16 - 2(2 -12)

                            = 4*2 + 2*16 - 2* (-10)

                             = 8 + 32 + 20

                             = 60

expand and simplify (x-3)(2x+1)(3x-2)

Answers

Answer:

6x³ - 19x² + x + 6

General Formulas and Concepts:

Algebra I

Terms/CoefficientsExpand by FOIL (First Outside Inside Last)

Step-by-step explanation:

Step 1: Define

(x - 3)(2x + 1)(3x - 2)

Step 2: Expand

Expand [FOIL]:                     (2x² + x - 6x - 3)(3x - 2)Combine like terms:            (2x² - 5x - 3)(3x - 2)Expand:                                6x³ - 15x² - 9x - 4x² + 10x + 6Combine like terms:            6x³ - 19x² + x + 6
Ya what they said above, I need em points

$2000 is invested at a rate of 4.2% compounded annually. Identify the compound interest function to model the situation. Then find the balance after 7 years. A = 2000(1.042)^t; $2667.50 A = 2000(1.42)^4t; $2557.50 A = 2000(1.042)^t; $2337.50 A = 2000(14.2)^4t; $2447.50

Answers

Answer:

A = 2000(1.042)^t; $2667.50

Step-by-step explanation:

The formula or model for Compound Interest is given as:

A = P(1 + r/n)^nt

Where:

A = Amount or Balance after t years

P = Principal or initial amount invested = $2000

r = Interest rate = 4.2% = 0.042

t = Time in years = 7 years

n = Compounding frequency = Annually = per year = 1

Hence, the compound interest function to model for the situation (Question) with time t above is:

A = 2000(1 + 0.042) ^1 ×t

A = 2000(1.042)^t

Therefore solving for the balance

A = 2000(1.042)^7

A = 2,667.50

A = $2667.50

Therefore, option a =

A = 2000(1.042)^t; $2667.50

is the correct option.

which the of triangles is similar to PQR​

Answers

Answer:

D

Step-by-step explanation

18/15=1.2

21/1.2=17.5

They Match!

9% ___ 0.4 will give brainliest



pls help :)

Answers

Answer:

9% is less than 0.4. 0.4 is really 4/10 which is 40% 40 is greater than 9 therefore 9% is less than 0.4! So your answer is 9%<0.4! I hope this helped!

Step-by-step explanation:

Simplify the expression:

7(1 + 8v)

Answers

7 ( 1  +  8 )

simplify

1. rearrange terms

7(1 + 8v)

7(8v + 1)

2. Distribute

7(8v + 1)

56v + 7

Solution

56v + 7

How can the slope of the line be interpreted? Every 98 words requires 312 minutes to read. Every 312 words requires 98 minutes to read. In each additional minute, approximately 98 more words are read. In each additional minute, approximately 312 more words are read.

Answers

Answer:

In each additional minute, approximately 312 more words are read.

Step-by-step explanation:

Given tbe sentences :

The slope is the rate of change per unit: in the context of the question, the number of word reads increases. By 312.

Hence, the slope according to the slope of the graph interpretation is that, the number of words read per minute increases by 312 as the value of minute increases by one minutes.

can anyone answer 2(3x+5)+7x and show work ?

Answers

Answer: -12 I believe I’m sorry if I’m wrong I’m not smart

Step-by-step explanation:

Simplifying

2(3x + -5) = 7x + 2

Reorder the terms:

2(-5 + 3x) = 7x + 2

(-5 * 2 + 3x * 2) = 7x + 2

(-10 + 6x) = 7x + 2

Reorder the terms:

-10 + 6x = 2 + 7x

Solving

-10 + 6x = 2 + 7x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7x' to each side of the equation.

-10 + 6x + -7x = 2 + 7x + -7x

Combine like terms: 6x + -7x = -1x

-10 + -1x = 2 + 7x + -7x

Combine like terms: 7x + -7x = 0

-10 + -1x = 2 + 0

-10 + -1x = 2

Add '10' to each side of the equation.

-10 + 10 + -1x = 2 + 10

Combine like terms: -10 + 10 = 0

0 + -1x = 2 + 10

-1x = 2 + 10

Combine like terms: 2 + 10 = 12

-1x = 12

Divide each side by '-1'.

x = -12

Simplifying

x = -12

Answer:

13x + 10

Step-by-step explanation:

First distribute, (2)(3x) + (2)(5) + 7x

This gives you 6x + 10 + 7x

Then combine then like terms 6x + 10 + 7x

To get (6x + 7x) + (10)

And a final answer of 13x + 10 :)

look at this please it would really help

Answers

i don’t know the answer to all but hopefully this will help u out a little bit:
0 hours would be 0 dollars of course
0.5 hours would be $2.50
1 hour would be $5
2 hours would be $10

GIVING BRAINLIEST PLEASE HELP

Answers

Answer:

The answer is B

Step-by-step explanation:

Answer:

ans is B sorry if it's direct

Help Fast. The question is in an image because there is a graph to see.

Answers

Answer:

the answer is (3, 2)

Step-by-step explanation:

the formula to find the centroid of a triangle is

{( x1+x2+x3)/3 , ( y1+y2+y3)/3}

UDD Question 6 10 pts Solve for x. Round to the nearest tenth (one decimal place). Just type the number, no unit of measurement. G X 240 DI F 48 Next * Previous​

Answers

Answer:

The answer is;

54.4

Step-by-step explanation:

The given parameter are;

Triangle ΔFGH = Right triangle

The length of segment [tex]\overline {FH}[/tex] = 48

The measure of ∠HFG = 28°

The measurement required = The measure of segment [tex]\overline {FG}[/tex] = x

The measure of ∠FHG = 90° angle opposite hypotenuse side of a right triangle

Therefore, ∠FGH = 180° - ∠HFG - ∠FHG = 180° - 90° - 28° = 62°

∠FGH = 62°

By sine rule, we have;

[tex]\overline {FH}[/tex]/(sin ∠FGH) = [tex]\overline {FG}[/tex]/(sin(∠FHG)

By substituting the known values, we have;

48/(sin 62°) = x/(sin(90°)

sin(90°) = 1, therefore, we have;

x/1 = x = 48/(sin 62°) = 54.4 (by rounding the answer to the nearest tenth)

x = 54.4

I know what the answer is but the teacher wants me to explain helpppppp

Answers

answer:   8

Steps / explaination

You are in the buy and sell business. find out the wholesale price of an item (e.g. t-shirt, soap,toy) suppose you buy 24 pieces of that item at wholesale price. atleast at what price should you tell each item to have a 25% profit? how much will be your total profit in pesos from these items?

With explanation please!!

Answers

The wholesale price isn't given, suppose the wholesale price is $5

Answer:

$6.25 ; 1441.8 pesos

Step-by-step explanation:

Number of items purchased = 24

Wholesale price of item = x

To obtain a 25% profit, the sales price would be :

Wholesale price = wholesale price + 25% of wholesale price

(x = x + 0.25x) per unit

For 24 items :

24x + 0.25 * 24x

Unit wholesale price = 5

24(5) + 0.25*24(5)

= $150

Hence, sale price per unit will be :

$150 / 24

= $6.25

Total profit in pesos :

1 dollar = 48.06 pesos

Total profit = $150 - 24(5) = $150 - $120 = $30

$30 = (30 * 48.06) = 1441.8 pesos

if there are 93 calories in 3/4 cups how many calories are in 1 cup

Answers

93 = 3/4
?? = 1
Cross multiple
1(93)/(3/4) = 124

Answer:

124

Step-by-step explanation:

Cross Multiply

(93x4)/3

I need help with this ASAP and can you explain so i can understand?!

Answers

Answer:

Adult tickets sold =  225

Student Tickets sold =  375

Step-by-step explanation:

Let:

Adult tickets sold = x

Student Tickets sold = y

Total tickets sold = 600

So, we can write: x+y = 600

Total money collected = 3037.50

Cost of 1 Adult ticket = $6.00

Cost of one Student ticket = $4.50

So, we can write: 6x+4.5y=3037.50

Now, we get a system of equations, that if solved we can find values of x and y

Let:

[tex]x+y = 600--eq(1)\\6x+4.5y=3037.50--eq(2)[/tex]

We can solve using substitution method.

Finding value of x from eq(1) and putting it in eq(2)

[tex]We\:have\\x+y=600\\x=600-y[/tex]

Put in eq(2)

[tex]6x+4.5y=3037.50\\6(600-y)+4.5y=3037.50\\3600-6y+4.5y=3037.50\\-1.5y=3037.50-3600\\-1.5y=-562.5\\y=\frac{-562.5}{-1.5}\\y=375[/tex]

So, we get value of y = 375

Now put value of y in eq(1) to find value of x

[tex]x+y=600\\Put\:y=375\\x+375=600\\x=600-375\\x=225[/tex]

So, we get value of x = 225

The Tickets sold will be:

Adult tickets sold = x = 225

Student Tickets sold = y = 375

In the hospital, 80 people were admitted Friday, 25% of these admissions were women in labor to have babies. How many women were in labor? O A 25 OB. 20 O C. 35 O D. 30

Answers

Answer:

Step-by-step explanation:

25% it means 1/4 of the total

1/4 of 80 is 20 (80/4=20)

answer B

Proving parallel lines

Answers

Answer:

Are you making a new post?

Step-by-step explanation:

7x^2a+7xa^2
Find the greatest common factor

Answers

Answer:

GCF is 7xa

Step-by-step explanation:

Answer:

hCf is 7ax

plz refer to the picture

plz mark as brainliest

pls help I literally don’t get this

Answers

I put in all doc!!! Lmk if u have questions

I don’t understand this

Answers

Answer:

your just finding area so

1.5×2.5=

1.5×1.5/2=

1.5×2.5=

I will put the answers in the comments I need to use a calculator

Answer:

Step-by-step explanation:

Think of it as two rectangles and one triangle.

The first rectangle is 1.5 * 2.5 = 3.75 square feet.

There is two of these rectangles, so you can do 3.75 *2 = 7.5 square feet.

Finally, the triangle is 1.5 by 1.5, so the area is 1.5 * 1.5 / 2 = 1.125.

To find the total area, add the two together: 7.5 + 1.125 = 8.625 square feet

Is x2 + 10x + 20 a perfect square trinomial?
Yes or no​

Answers

Answer:

=

(

x

5

)

2

Step-by-step explanation:

=(x-5) exponent 2

Yes

No, x² + 10x + 20 is not a perfect square trinomial.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

Given:

A quadratic polynomial,

x² + 10x + 20.

A perfect square trinomial is an expression that may be constructed from the binomial equation's square.

That means, the roots are repeated.

Solving the equation, we get,

x = (-5 ± √5)

The roots are not repeated.

Therefore, it is not a perfect square trinomial.

To learn more about the quadratic function;

https://brainly.com/question/11485644

#SPJ2

Which graph represents the system of inequalities?


3x+5y<10

x−y≤1

Answers

Answer:

I believe it's the one on the bottom left

Step-by-step explanation:

I'm still taking my test so I'll come back later to tell you if it's correct.

Answer:

It's the one on the bottom left

Step-by-step explanation:

What is the solution of the system of equations shown in the graph below?

Answers

Answer:

Answer is (-1,-2) As where 2 lines bisect, that point be the answer. And in given scenario, both the lines bisected at (-1,-2)

Step-by-step explanation: