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Given the following exponential function, identify whether the change

anzhelika [568]

Answer:

Growth, with a 9% increase.

Step-by-step explanation:

Exponential patterns are usually defined by some kind of repeated multiplication. In most exponential patterns we start with some initial value (let's call it a) and some multiplier (let's call it b), and a is multiplied by b some number x times. We capture this as a function y with the equation $y=ab^x$ There are three broad categories for this pattern:

No growth/decay - The function has an initial value that never changes. In order for the initial value to stay constant, we need $b=1$ , since multiplication by 1 doesn't change the number it's multiplied by.
Growth - The function grows at some exponential rate; for every increase in x, our initial value will be at least as big as it was for smaller values of x, so $b>1$ in this case. (Example: A bacteria population starts at size 3 and doubles in size every hour; after x hours, there will be $3\cdot2^x$ bacteria)
Decay - The function decays or decreases at some exponential rate; for every increase in x it can't be as large as it was for smaller values of x, so $b$ here. (Example: An Instagram post gets an initial wave of 100 new likes, and every hour it gets half the number of likes as the previous hour, so the number of new likes per hour is $100\cdot(0.5)^x$ .

In the function $y=210(1.09)^x$ , $b>1$ , so we have exponential growth, but by what percent? Well, for every step in x, we take 1.09 (109%) of the previous value, so that's a 9% increase.

4 0

3 years ago

A pinwheel design for a quilt is shown at the right. Each square of the design has a side length of 3 inches. May someone help m

arlik [135]

Answer:

Part A) The area total of the design is $144\ in^{2}$

Part B) The total area of the four large shaded triangles is $72\ in^{2}$

Part C) The cost to purchase the material to make the triangles for the quilt will be $\$172.8$

Step-by-step explanation:

Part A) Find the area total of the design

The area total of the design is a square

so

To find the length side of the square design multiply the number of squares by 3 in

$a=(4*3)=12\ in$

$A=(a)^{2}$

$A=(12)^{2} =144\ in^{2}$

Part B) Find the total area of the four large shaded triangles

the area of the four large triangles is equal to

$A=4[\frac{1}{2}(b)(h)]$

we have that

$b=(2*3)=6\ in$

$h=(2*3)=6\ in$

substitute

$A=4[\frac{1}{2}(6)(6)]=72\ in^{2}$

Part C) How much will it cost to purchase the material to make the triangles for the quilt ?

To find the cost multiply the area of each design of four large triangles by 30 and then multiply by $0.08 per square inch

The cost is equal to

$30(0.08)(72)=\$172.8$

4 0

3 years ago

A kennel owner has 400 feet of fencing to enclose a rectangular dog exercise pen. Express the area of the exercise pen, A, as a

DENIUS [597]

Answer:

A(x) = x(200-x)

Step-by-step explanation:

400 feet of fencing to enclose a rectangular dog exercise pen means the perimeter of rectangle is 400 feet

If x is length and y is breadth. Perimeter is given by :

P = 2(x+y)

400 = 2(x+y)

⇒ (x+y) = 200 .....(1)

y = 200-x

Area of a rectangle is given by :

A = xy

A(x) = x(200-x)

Hence, the area as a function of length of rectangle is x(200-x).

3 0

3 years ago

1. 248 + 56 base 8 2. 751 +24 base 4 3. 1001 _ 111 base 3 4.3121 _1334 base 5 5. 321 ×21 base 5 6. 205+ 51 base 6

liraira [26]

Answer:

If we are converting between two bases other than decimal, we typically have to convert ... For two digits in base 8, we need 4, 5, or 6 digits in base 2.

5 0

3 years ago

The rarest form of dichromatism is _____.?

zubka84 [21]

The rarest form of dichromatism is = tritanopia

5 0

3 years ago