The population, P, of six towns with time t in years are given by the following exponential equations:
(i) P = 1000 (1.08) Superscript t (ii) P = 600 (1.12) Superscript t
(iii) P = 2500 (0.9) Superscript t (iv) P = 1200 (1.185) Superscript t
(v) P = 800 (0.78) Superscript t (vi) 2000 (0.99) Superscript t
Which town decreasing the fastest?
a.
ii
c.
iii
b.
v
d.
vi



Please select the best answer from the choices provided


A
B
C
D

Answers

Answer 1

Given:

The population, P, of six towns with time t in years are given by the following exponential equations:

(i) [tex]P=1000(1.08)^t[/tex]

(ii) [tex]P = 600 (1.12)^2[/tex]

(iii) [tex]P =2500 (0.9)^t[/tex]

(iv) [tex]P=1200 (1.185)^t[/tex]

(v) [tex]P=800 (0.78)^t[/tex]

(vi) [tex]P=2000 (0.99)^t[/tex]

To find:

The town whose population is decreasing the fastest.

Solution:

The general form of an exponential function is:

[tex]P(t)=ab^t[/tex]

Where, a is the initial value, b is the growth or decay factor.

If b>1, then the function is increasing and if 0<b<1, then the function is decreasing.

The values of b for six towns are 1.08, 1.12, 0.9, 1.185, 0.78, 0.99 respectively. The minimum value of b is 0.78, so the population of (v) town  [tex]P=800 (0.78)^t[/tex] is decreasing the fastest.

Therefore, the correct option is b.


Related Questions

On another map, the distance between Saugerties and
Kingston is 2 inches. What would the distance from
Saugerties to Catskill be on this map?

Answers

Answer:

10miles

Step-by-step explanation:

Answer:

I have no clue what is going on wit dis g

Find the measure of <3. 90 50 40 130

Answers

Answer:  90 degrees

=============================================================

Explanation:

This figure is a kite since we have two pairs of adjacent sides that are congruent, but not all sides are the same length.

One property of kites is that the diagonals are always perpendicular (this applies to rhombuses as well). This means angle 3 is 90 degrees.

The measure of ∠3 is 90°

Because in a kite the diagonals bisects at 90°

Therefore ∠3 is 90°

Answered by Gauthmath must click thanks and mark brainliest

Evaluate the expression when x=-6.
x² + 5x-2

Answers

Answer:

Step-by-step explanation:

Hello!

x² + 5x-2

6² + 5*6 -2 =

36 +30 -2 =

66 -2=

64

(-6)^2+5(-6)-2
36-30-2
36-32= 4

What is the period of the graph of y=1/2 sin (2πx) -3?
A. 1
B. 1/2
C. 3
D. 2π

Answers

Answer:

A. 1

Step-by-step explanation:

Since this graph is in the form A sin (B(x+c))+d, where

the amplitude is the absolute value of AThe period is 2pi/BPhase Shift is CMidline is y=D

Therefore, the values are

A=1/2

B=2pi

C=0

D=-3

So the period is 2pi/2pi which is 1.

Dont give me wrong answers. please help though.​

Answers

Answer:

24 in^3

Step-by-step explanation:

Volume of the figure= 3 * (Volume of a cube with side 2)

Volume of the figure= 3*2^3=24 in^3

Answer:

24 cubic inches

Step-by-step explanation:

The formula for finding volume is b*h*w.

b*h*w is base multiplied my height multiplied my width. Lets use this formula to find the volume of one of cubes.

Here is the information we know about the cubes:

the base is 2 inches

the height is 2 inches

the width is 2 inches

Lets put this information into the formula to find the volume of one of the cubes. I will show the work in steps so it is easy to follow.

Step one: plug the given information into the formula.

b*h*w = 2*2*2

Step two: Solve the equation.

2*2*2 = 4*2 = 8

Now we have the volume of one on the cubes. This is 8 cubic inches. However, to find the volume of all three of the cubes we must multiply 8 by 3.

Step three: multiply 8 by 3.

8*3 = 24

And there you have it! Our final answer is 24 cubic inches.

Here is a quick review of what we did to get our answer:

2*2*2 = 8

8*3 = 24

I hope this helps!

17. ralph is 3 times as old as sarah. in 4 years ralph will only be twice as old as sara will be then. find ralph’s age now.

Answers

Answer:

Sara is now 4, will be 8 in 4 years. Ralph is now 12, will be 16 in 4 years.

What is the solution to the system that is created by the equation y = - x + 6

Answers

Answer:

If you draw the graph of y = -x + 6  on the above graph  the solution to system will be the coordinates of the point of intersection.

the equation of the line drawn above is y = 0.5x

so you can also find the solution by solving the system

y = 0.5x

y = -x + 6

0.5x = -x + 6

1.5x = 6

x = 6/1.5 = 4

and y = 0.5*4 = 2

The answer is  (4, 2)     - the third choice.

Step-by-step explanation:

.The conversion of square feet to square yards can be represented by direct variation. Three square yards are equivalent to 27 square feet. Let y represent the number of square yards and x the number of square feet. Then y varies directly with x.

What is the constant of variation?



What is the equation representing the direct variation?

Answers

Answer:

The constant of variation is 1/9

The equation representing the direct variation is y/x= 1/9

Step-by-step explanation:

In direct variation, y/x=k denotes the equation, with k being the constant of variation. Here, y is the number of square yards and x is the number of square feet. Therefore, as we know that 27 square feet = 3 square yards, we can write one point (x₁, y₁) as (27 square feet, 3 square yards). Plugging x₁ and y₁ into our equation, we get

y/x = k

3 / 27 = k

(3/27) / (3/3) = 1/9* = k

Therefore, the constant of variation is 1/9

Next, as stated previously, y/x = k represents the equation of direct variation. Therefore, y / x = 1/9 as our equation

* because 3 is a factor of both 3 and 27, we can divide both the numerator and denominator by 3 to keep the fraction the same but also simplify it. One way to find the greatest common factor is to list the factors of each number and see the highest number that is a factor of both

The constant of variation is "1/9" and the equation representing the direct variation is y = (1/9)x.

What is the equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation of direct variation is given by,

y = kx   ....(i)    where "k" is a constant.

Let y represent the number of square yards and x the number of square feet. Then y varies directly with x.

Given that y varies directly with x, and x = 27, then y = 3.

Substitute the values of y = 3 and x = 27 in the direct variation equation and solve for k:

⇒ 3 = 27k

⇒ k = 3/27

⇒ k = 1/9

Substitute the values of k = 1/9 in the direct variation equation :

⇒ y = (1/9)x

Thus, the constant of variation is "1/9" and the equation representing the direct variation is y = (1/9)x.

Learn more about the equations here:

brainly.com/question/10413253

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PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
The students in Shawn's class got to choose whether to visit the zoo or the aquarium. 3 students went to the zoo and 15 students went to the aquarium. What is the ratio of the number of students who went to the zoo to the number of students who did not go to the zoo?
A. 1:6
B. 1:1
C. 1:3
D. 1:5

Answers

Answer:

1 : 5

Step-by-step explanation:

3 students zoo

15 students aquarium

zoo : not zoo

3: 15

Divide each side by 3

3/3 : 15/3

1 : 5

Will Mark Brainlest Help pls​

Answers

Answer:

Hello,

[tex]\begin{bmatrix}-2&2\\3&5\\\end{bmatrix}\\\\[/tex]

Step-by-step explanation:

[tex]\begin{bmatrix}2&3\\5&7\end{bmatrix}-A=\begin{bmatrix}3&1\\-2&-3\end{bmatrix}+\begin{bmatrix}1&0\\0&1\end{bmatrix}\\\\\\\begin{bmatrix}2&3\\5&7\end{bmatrix}-A=\begin{bmatrix}2&3\\5&7\end{bmatrix}-\begin{bmatrix}4&1\\-2&-2\end{bmatrix}\\\\\\A=\begin{bmatrix}-2&2\\3&5\end{bmatrix}\\\\[/tex]

Look at the figure. Which step should be taken next to construct a line through point R that is perpendicular to ST ?

Answers

Answer:

where is the figure without figure how to find out

Explain how to solve the equation
.
b – 7 = 12

Answers

Answer:

19

Step-by-step explanation:

Add 7 onto 12 to find answer.

Answer:

b = 19

Step-by-step explanation:

b = 12 + 7

Simplify 12+7 to 19.

Each coffee pot hold 6 cups of coffee we sell 10 cups of coffee every fifteen minutes how many pots of coffee do I need to make in an hour?

Answers

Answer:

7 pots of coffee (If you want to be precise its 6 2/3)

Step-by-step explanation:

So basically you need 10 cups of coffe in fifteen minutes, so 60/15=4 then time 10. so 40 is how much coffee you need in a hour, but we are solving the pot so 40/6= 6 2/3. but it says how many pots so we round it up so its 7. (Unless you wanna be precise)

1 hour=60 minutes
every 15 min, 10 sold
60/15=4
4(10)=40 sold in 1 hour
1 pots=6 cups
1/x=6/40
x=6.6
pots must be integer
x=7
number of pots of coffee is 7

Select all decimals that are equivalent to
(
9
×
100
)
+
(
2
×
10
)
+
(
3
×
1
10
)
+
(
5
×
1
100
)
.
A.
92.35

B.
920.350

C.
902.35

D.
92.350

E.
920.35

F.
920.035 I really need help

Answers

Answer:

B, E

Step-by-step explanation:

( 9 × 100 )  +  ( 2 × 10 )  +  ( 3 × 0.10 )  +  ( 5 ×0.01 )  = 920.35

A.  92.35

B.  920.350

C.  902.35

D.  92.350

E.  920.35

F. 920.035

Can anyone please help?

Answers

Answer:

i don't know

( lol )

heheeeee

6. Solve for x!! please help!

Answers

x/2 = -7

=> x = -7 × 2

=> x = -14

Answer:

x=-14

Step-by-step explanation:

[tex]\frac{x}{2} =-7\\\\x=-14\\[/tex]


Find the value of z
A.110
B.141
C.80
D.100

Answers

Answer:

Option A 110degree is the answer

Does this graph show a function? Explain how you know.
A. No; the graph fails the vertical line test.
• B. No; there are y-values that have more than one x-value.
• C. Yes; the graph passes the vertical line test.
D. Yes; there are no y-values that have more than one x-value.

Answers

Answer:

C. Yes; the graph passes the vertical line test.

Step-by-step explanation:

Reasons the others are wrong:

A. It does pass the vertical line test.

B. Y-values can have any x values. It is x-values that can't have multiple y-values.

D. There are y-values with more than one x-value on this graph so that's just false. Even if it were true, that still doesn't invalidate it due to the reasons given in Answer B.

HELP PLS HELP MEEEEE IM FAILING PYTHAGOREAN THEOREM

Answers

7^2 + 6^2 = h^2

49 + 36 = h^2

85 = h^2

√85 = h

h = 9.21m

Answered by Gauthmath must click thanks and mark brainliest

I need help ASAP!!! FIND THE SEGMENT Please explain how u got the answer

Answers

Answer:

x = 960

Step-by-step explanation:

Using the Altitude- on- Hypotenuse theorem

( leg of large triangle )² = ( part of hypotenuse below it) × ( whole hypotenuse), so

x² = 576 × (576 + 1024) = 576 × 1600 = 921600 ( take square root of both sides )

x = [tex]\sqrt{921600}[/tex] = 960

Find the slope of the line that passes through (-26, 9) and (32, 71).

Answers

Answer:

[tex]Slope = \frac{31}{29}[/tex]

Step-by-step explanation:

Step 1:  Define the slope formula

[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Step 2:  Find the slope

[tex]Slope = \frac{71-9}{32-(-26)}[/tex]

[tex]Slope = \frac{62}{58}[/tex]

[tex]Slope = \frac{31}{29}[/tex]

Answer:  [tex]Slope = \frac{31}{29}[/tex]

Please help me to solve this question as soon as possible. Thank you
1.6 is a common factor of 36 and y. Find the possible value of y.
A. 25
B. 48
C.57
D. 81

Answers

Answer:

the answer is B

Step-by-step explanation:

because only 48 is dividable by 6


Find the measure of

Answers

Answer:

74 degrees

.................

Answer:

74

Step-by-step explanation:

BEC and CED form a straight line so they add to 180

BEC+CED = 180

106+ CED = 180

CED = 180-106

CED = 74

Sammy and Hannah are finalists in a cooking competition. For the final round, each of them will randomly select a card without replacement that will reveal what their star ingredient must be. Here are the available cards:
Cabbage
Spinach
Kale
Leeks
Carrots
Turnips

Cabbage


Leeks




Spinach


Carrots




Kale


Turnips




Sammy and Hannah both want to get leeks as their star ingredient. Sammy will draw first, followed by Hannah.
What is the probability that NEITHER contestant draws leeks?
Round your answer to two decimal places.

Answers

The probability that neither of them draws the Leeks card is P = 4/6 = 0.667

Here we can assume that all the cards have the same probability of being randomly drawn.

The cards are:

Cabbage Spinach Kale Leeks Carrots Turnips

So we have 6 cards. We want to find the probability that neither contestant draws the "Leeks" card.

Sammy draws first, the probability of drawing the Leeks card will be equal to the quotient between the number of Leeks cards (one) and the total number of cards (6).

Then the probability of drawing the leeks card is p = 1/6

This means that the probability of NOT drawing the leeks card is:

q = 1 - 1/6 = 5/6.

Now draws Hanna, now there are 5 cards in the deck (because one was already drawn). With the same approach as before, the probability of drawing the Leeks card is p = 1/5, then the probability of NOT drawing the card is:

q = 1 - 1/5 = 4/5.

The joint probability (this is, the probability of both of these events to happen together) is just the product of the individual probabilities.

Then the probability that neither of them draws the Leeks card is:

P = (4/5)*(5/6) = 4/6 = 0.667

If you want to learn more about probability, you can read:

https://brainly.com/question/24349426

Write an inequality and show on a number line all numbers:
less than 4 but greater than or equal to 0

Answers

Answer:

the inequality is 0<x<4

Step-by-step explanation:

(0,4)

Categorize the graph as linear increasing, linear decreasing, exponential growth, or exponential decay

Answers

Answer:

D. Exponential growth

Step-by-step explanation:

Hope this helps

Function that is similar to exponential.

Option (A) is correct.

What is exponential decay?

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula  [tex]y=a(1-b)^{x}[/tex] wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed.

We can observe that

First, y increases as x increases

Last it is a function that is similar to exponential.

Function is an exponential decay.

Option (A) is correct.

Find out more information about exponential decay here

https://brainly.com/question/14355665

#SPJ2

Please help me solve this!

Answers

Answer:

Step-by-step explanation:

Reference angle = 27

height = 2

Sin(27) = opposite / hypotenuse

hypotenuse = opposite / sin(27)

opposite = 2

hypotenuse = 2 / sin(27)

hypotenuse = 4.405

The ramp has to be 4.41 feet long.

Can someone plz help me

Answers

Answer:

37500

Step-by-step explanation:

pattern is multiplying by -5.

-7,500*-5 = 37,500

Have a nice day! :-)

How many significant digits are there in the number 1.00250? OA) 7 OB) 6 OC) 5 OD) 4​

Answers

Answer:

OB

Step-by-step explanation:

start counting from 1

Then your significant digit is 6

find the missing side.​

Answers

Answer:

I htink x ≈ 8

Step-by-step explanation:

Answer:

X is approximately 7.8.

Step-by-step explanation:

You can use SOH-CAH-TOA to help figure out what function (sin, cos, tan) you need to use in order to figure out the missing side.

For this one, we can see the angle is pointing to the opposite side (x length), and we have been given the hypotenuse (18). So we want to use the sin function.

[tex]sin\ (angle)=\frac{opposite}{hypotenouse}[/tex]

[tex]sin (26)=\frac{x}{18}[/tex]

[tex]0.438=\frac{x}{18}[/tex]

[tex]7.890... = x[/tex]

Using Pythagorean theorm, you can figure out the other side if need be :)

For reference:

[tex]sin (angle)=\frac{opposite}{hypotenuse}[/tex]

[tex]cos(angle)=\frac{adjacent}{hypotenuse}[/tex]

[tex]tan(angle)=\frac{opposite}{adjacent}[/tex]

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