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2 years ago

The function f(x)=501170〖(0.98)〗^x gives the population of a Texas city x years after 1995.

Mathematics

1 answer:

Maurinko [17]2 years ago

6 0

Answer:

The population in 1995

501170

Is the population increasing or decreasing?

The population is decreasing

The rate of population change

$-10124.99(0.98^{x} )$

population in the year 2020

302439

Step-by-step explanation:

Since 1995 is the base year, the population in 1995 is simply found by setting x equal to 0 in the given function;

$f(0)=501170(0.98^{0})=501170$

The population is clearly decreasing over time since the base of the exponent, 0.98, is less than 1.

The rate of population change is obtained by differentiating the function with respect to x using the rule;

$if y=a^{x}\\\frac{dy}{dx}=a^{x}*lna\\$

The population in the year 2020 is obtained by setting x equal to 25 in the population function since 2020-1995 = 25;

$f(25)=501170(0.98^{25}) =302439$

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In a group of 60 workers they get paid an average of 80$ a day per person.

hichkok12 [17]

Answer:

48 workers earn $75 a day.

Step-by-step explanation:

Let x people earn 75 a day then 60-x earn 100 dollars a day.

Average is $80 a day so total paid out to the 60 workers

= 60*80 = $4800.

So 75x + 100(60-x) = 4800

75x + 6000 - 100x = 4800

6000 - 4800 = 100x - 75x

1200 = 25x

x = 48.

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1 year ago

F(x) = x² + 5x-1 is shifted 3 units right. The result is g(x). What is g(x)?

CaHeK987 [17]

Answer:

Step-by-step explanation:

When a function is being shifted to the left, all x values will be added by y units shifted. (The constant that comes with x is excluded, eg. 3x shifted by 2 units left, becomes 3(x+2) and not 3x+2.)

Likewise, when a function is being shifted to the right, all x values will be subtracted by y units shifted. (Constant rules applies as well.)

Given f(x) is shifted 3 units right,

the new function, g(x) becomes:

$g(x) = {(x - 3)}^{2} + 5(x - 3) - 1$

Therefore the answer is D in this case.

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1 year ago

A store offers a 15% discount on their pants. If the pants originally cost $30.00 what will be the discount price of the pants?

d1i1m1o1n [39]

Answer:

The pants will either be 25.50 or 4.50. Sorry I'm not sure if 15% off 30.00 is the number minus the original price or not.

Step-by-step explanation:

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2 years ago

Answer question 12 and 13

ale4655 [162]

12) The mistake that Liz made was instead of shading in 5% of the diagram, she shaded in 5 blocks, which is incorrect.
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2 years ago

Would someone please help me solve these questions?~

olasank [31]

Question # 17

Solution:

Graphing the vertices of a triangle and transforming by first translating

(x, y) → (x -3, y - 3) and then reflecting in the line y = x.

As A(-1, 1), B(0, 3) and C(3, 4)

After Translation: (x, y) → (x - 3, y - 3)

A(-1, 1) → A'(-4, -2)

B(0, 3) → B'(-3, 0)

C(3, 4) → C'(0, 1)

After Reflection: in the line y = x

The reflection of the point (x, y) across the

line y = x is the point (y, x).

A'(-4, -2) → A''(-2, -4)

B'(-3, 0) → B''(0, -3)

C'(0, 1) → C''(1, 0)

Pleas check the top right side of the attached figure a.

Is the image same if the order of the transformation is switched ? (Reflection, then glide). Changing the order of transformation.

A(-1, 1), B(0, 3) and C(3, 4) 

 After Reflection: in the line y = x

The reflection of the point (x, y) across the line y = x is the point (y, x).

A(-1, 1) → A'(1, -1)

B(0, 3) → B'(3, 0)

C(3, 4) → C'(4, 3)

After Translation: (x, y) → (x - 3, y - 3)

A'(1, -1) → A''(-2, -4)

B'(3, 0) → B''(0, -3)

C'(4, 3) → C''(1, 0)

No, the image is no longer the same if order of the transformation is switched as shown at the right bottom of figure a.

Answering the YES and NO Questions:

<h3>Is the composition a glide reflection?</h3>

No, the composition is not a glide reflection as glide reflection is commutative. If we reverse the direction of the composition, the outcome will be affected.

Check the figure at top right side of figure a, and compare it with the figure at the bottom right side of figure a. They are not the same.

<h3></h3><h3>Is the image same if the order of the transformation is switched ? (Reflection, then glide)</h3>

No, the image is no longer the same if order of the transformation is switched as shown at the right bottom figure of figure a.

The top right side of figure a was transformed after first translation of (x, y) → (x - 3, y - 3) and then doing reflection across the line y = x. While the bottom right side of figure a was made by first reflection across the line y= x and then translation of (x, y) → (x - 3, y - 3. So, after changing the order both figures do not remain the same.

Question # 18

Solution:

Graphing the vertices of a triangle and transforming by first 90 rotating clockwise and then reflection in the y axis.

A(-1, 1), B(0, 3) and C(3, 4)

After transforming by first 90 rotating clockwise about the origin. The new position of point (x, y) will be (y, -x)

A(-1, 1) → A'(1, 1)

B(0, 3) → B'(3, 0)

C(3, 4) → C'(4, -3)

After Reflection: in the line y axis

The reflection of the point (x, y) in the line line y-axis is the point (-x, y).

A'(1, 1) → A''(-1, 1)

B'(3, 0) → B''(-3, 0)

C'(4, -3) → C''(-4, -3)

Please check the top right side of figure b.

If the order of the transformation were performed in reverse order ? (Reflection, then rotation), would the final image by the same?

A(-1, 1), B(0, 3) and C(3, 4)

After Reflection: in the line y-axis

The reflection of the point (x, y) in the line y-axis is the point (-x, y).

A(-1, 1) → A'(1, 1)

B(0, 3) → B'(0, 3)

C(3, 4) → C'(-3, 4)

After transforming by first 90 rotating clockwise about the origin. The new position of point (x, y) will be (y, -x)

A'(1, 1) → A''(1, -1)

B'(0, 3) → B''(3, 0)

C'(-3, 4) → C''(4, 3)

Answering the YES and NO Questions:

If the transformation were performed in reverse order (reflection. then rotation), would the final image be the same?

No, if we reverse the direction of the composition, the final image would not be same.

Check the figure at top right side of figure b, and compare it with the at the bottom right side of figure b. They are not the same.

Would the reflection of triangle ABC in the line y = x have produced the same final image?

Yes, the reflection of triangle ABC in the line y = x would have produced the same final image. Compare the figure of the bottom left with the bottom right of figure b.

As A(-1, 1), B(0, 3) and C(3, 4)

After Reflection: in the line y = x

The reflection of the point (x, y) across the

line y = x is the point (y, x).

A(-1, 1) → A''(1, -1)

B(0, 3) → B''(3, 0)

C(3, 4) → C''(4, 3)

Hence, the reflection of triangle ABC in the line y = x would have produced the same final image. Compare the figure of the bottom left with the bottom right of figure b.

Keywords: transformation, reflection, rotation, translation, triangle

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3 0

3 years ago