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2 years ago

Construct the exponential function that contains the points (0,2) and (3,54)

Mathematics

1 answer:

erma4kov [3.2K]2 years ago

8 0

The exponential function that passes through (0,2) and (3,54) is a growth function

The exponetial function is y = 2 * 3^x

<h3>How to construct the exponential function?</h3>

The points are given as:

(x,y) = (0,2) and (3,54)

An exponential function is represented as:

y = ab^x

Substitute the points in the equation

2 = ab^0 and 54 = ab^3

Solve 2 = ab^0

a = 2

Substitute 2 for a in 54 = ab^3

54 = 2b^3

Divide by 2

27 = b^3

Take the cube roots of both sides

b = 3

So, we have:

y = ab^x

This becomes

y = 2 * 3^x

Hence, the exponetial function is y = 2 * 3^x

Read more about exponential functions at:

brainly.com/question/24077767

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4 years ago

Challenge Yael used to have a square garage with 370 ft ^2of floor space. She recently built an

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Scale factor of area is the square of the scale factor of length

The required values are;

The length of one sides of the garage was originally approximately 19.2 ft.

The length of one of the sides of the garage is now approximately 23.6 feet long

The percentage increase in length is approximately 22.5 %

Reason:

The given parameters are;

The area of the square garage = 370 ft.²

The area of the new garage has 50% more space

Required;

Part A

The initial side length

The initial side length, given to the nearest tenth, s, is the square root of the area, A, given as follows;

s = √(370 ft.²) ≈ 19.2 ft.

Part B

The side was increased by 50%, to give,

370 + 0.5×370 = 555

The new area of the garage = 555 ft.²

The side length of the new garage, s = √(555) ≈ 23.6

The side of the garage now is 23.6 ft.

Part C

The percentage increase is given as follows;

$The \ percentage \ increase \ in \ length = \dfrac{New \ length - Initial \ length}{Initial \ length }$

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The percentage increase in length of the side of the garage is approximately 22.5 %

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3 years ago

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3 years ago

Use linear combination to solve this problem. show your work. 3x + 2y = -4 4x - y = 13

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Answer:

The solution of the system of equations is the point $(2,-5)$

Step-by-step explanation:

we have

$3x+2y=-4$ -----> equation A

$4x-y=13$ -----> equation B

Multiply the equation B by 2 both sides

$2*(4x-y)=2*13$

$8x-2y=26$ ------> equation C

Adds equation A and equation C

$3x+2y=-4\\8x-2y=26\\----------\\3x+8x=-4+26\\11x=22\\x=2$

Find the value of y

Substitute the value of x in equation A

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3 years ago