The population P (in thousands) of a certain city from 2000 through 2014 can be modeled by P = 160.4ekt, where t represents the year, with t = 0 corresponding to 2000. In 2007, the population of the city was about 162,075. Find the k value

Answers

Answer 1

Answer:

The k value is [tex]k = 0.0015[/tex]

Step-by-step explanation:

Population:

The population P(in thousands), of the city, in t years after 2000, is given by the following equation:

[tex]P(t) = 160.4e^{kt}[/tex]

In 2007, the population of the city was about 162,075.

This means that [tex]P(7) = 162.075[/tex], that is, when [tex]t = 7, P(t) = 162.075[/tex]

Find the k value

[tex]P(t) = 160.4e^{kt}[/tex]

[tex]162.075 = 160.4e^{7k}[/tex]

[tex]e^{7k} = \frac{162.075}{160.4}[/tex]

[tex]\ln{e^{7k}} = \ln{\frac{162.075}{160.4}}[/tex]

[tex]7k = \ln{\frac{162.075}{160.4}}[/tex]

[tex]k = \frac{\ln{\frac{162.075}{160.4}}}{7}[/tex]

[tex]k = 0.0015[/tex]

The k value is [tex]k = 0.0015[/tex]


Related Questions

When a fair die is rolled, find the probability of rolling the following:

2 or 6

Answers

I think it would be an 2

What is the complete factorization of x2 + 4x − 45?

Answers

Answer:

(x-5) (x+9)

Step-by-step explanation:

what multiplies to -45 but adds to positive 4?  -5 and 9. that's how you get (x-5) (x+9)

simplify
3a + 2b - 8a + b

Answers

Answer:

-5a+3b

Step-by-step explanation:

just adding and subtracting like terms

Answer:

3b-5a

Step-by-step explanation:

hope this helps:)

Question 19:
1 point
In the diagram below of circle O, chords JT and ER intersect at M.
E
М.
M
ºo
R
If EM = 8 and RM = 15, the lengths of JM and TM could be
(1) 12 and 9.5
(3) 16 and 7.5
(2) 14 and 8.5
(4) 18 and 6.5

Answers

Applying the intersecting chords theorem, the possible lengths of JM and TM could be: 16 and 7.5.

What is the Intersecting Chords Theorem?

The intersecting chords theorem states that product of the divided segments of each intersectint chords are equal to each other.

Based on the intersecting chords theorem, we would have:

(EM)(RM) = (JM)(TM)

If JM and TM are 16 and 7.5 respectively, we would have:

(8)(15) = (16)(7.5)

120 = 120

The lengths of JM and TM could therefore be: 16 and 7.5.

Learn more about the intersecting chords theorem on:

https://brainly.com/question/13950364

#SPJ2

Answer:

16 and 7.5

Step-by-step explanation:

need help? will get brainlylist

Answers

Answer:

its the first answer.

hope this helps you a lot.

Chord is a line that joins any two points on the circle

AC,BC

OPTION A is the correct answer

Determine the value for x in the picture below.

Answers

Answer:

x=9

Step-by-step explanation:

Similar triangles

8/20 = 6/(x+6)

==> 2/5 = 6/(x+6)

2/5x+12/5=6

2/5x=18/5

x=9

Answer is x = 6
I hope that helps

Question and choices are in the photo please explain the answer

Answers

Answer:

336

Step-by-step explanation:

The exclamation mark in math represents the factorial operation, which means you multiply the number by decreasing positive integers.

Therefore:

5! = 5 x 4 x 3 x 2 x 1 = 120.

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320

8!/5! = 40320/120

40320/120 = 336

WILL GIVE BRAINLIEST

Answers

Answer:

Should be $300

let me know if it's correct:)

the answer is 300
because 96 x 3 = 288
204 x 3 = 612

when you minus 288 - 612 the answer is 324 and the estimate is 300

SOMEONE PLEASE HELP ME I DONT KNOW HOW TO DO THIS TYPE OF PROBLEM

Answers

Answer:

Step-by-step explanation:

Because angles SQR and RQT are central angles, they are congruent to the arcs they intercept. This means that arc SR = 101 and arc RT = 118, making the whole major arc SRT = 219. That means that the minor arc, ST is 360 - 219 which is 141. We are looking in particular for the measure of angle SRT. It just so happens that angle SRT is an inscribed angle, so by definition it is one-half the measure of the arc it intercepts. It intercepts arc ST which we found measures 141, so angle SRT is 141/2 = 70.5

-3 (7x + 7) = -38 - 4x

Answers

Answer:

x = 1

Step-by-step explanation:

-3 (7x + 7) = -38 - 4x

-3(7x)-3(7) = -38 - 4x

-21x - 21 = -38 - 4x

-21x+4x = -38+21

-17x = -17

x = -17/-17

x = 1

Answer:

x = 1.

Step-by-step explanation:

-3(7x + 7) = -38 - 4x

Use distributive property to get:

-21x - 21 = -38 - 4x

Add 4x to both sides to get:

- 17x - 21 = -38

Add 21 to both sides to get:

- 17x = -17

x = 1.

I hope this helps, have a nice day.

The graph of a function is a parabola that has a minimum at the point (-3,9). Which equation could represent the function?

Answers

Well there are no choices listed so it's going to be hard to say which; we'll write an expression for all of them and then give a few instances.

A parabola with a minimum forms a CUP, concave-up positive, meaning the coefficient a on x² must be positive, a>0.  

The general form with vertex (p,q) is

y = a(x-p)² + q

So for us, all our parabolas are of the form

y = a(x- -3)² + 9

y = a(x² + 6x + 9) + 9

y = ax² + 6ax + 9(a+1)

That's the general form for a parabola with vertex (-3,9); a>0 assure the parabola has a minimum at the vertex.

Some instances:

a=1 gives

Answer: y = x²+6x+18

a=4 gives

y = 4x² + 24x + 45

Other positive as give other possible answers; without the choices it's impossible to know which one they're seeking.

How many tiles would be in figure 100? Help :/

Answers

Answer: pretty sure it is 201 tiles

please mark me brainlies. That would be helpful

Find the value of x that will make line u parallel to line v. Show all of your work

Answers

Answer:

x = - 11

Step-by-step explanation:

u and v are parallel if you  have equal alternate interior angles .

that is ,

x + 111 = 100

x = 100 - 111

x = - 11

What is the value of the expression 5x2-8x+4 when x = -3

Answers

Answer:

5 x 2 - 8x + 4

5 x 2 - 24 + 4

10 - 24 + 4

-10

Answer: -10

PLEASE HELPP
use the spinner to find the odds in favor of stopping on a multiple of 6

Answers

1 and 9 are the awnser

In a biscuit tin, there are 10 chocolate and 4 shortbread biscuits. What proportion are, a) Chocolate ?

Answers

Answer:

Proportion of chocolate in biscuit tin = 5:7

Step-by-step explanation:

Given:

Number of chocolate in biscuit tin = 10

Number of shortbread biscuits in biscuit tin = 4

Find:

Proportion of chocolate in biscuit tin

Computation:

Proportion of chocolate in biscuit tin = Number of chocolate in biscuit tin / Total product in biscuit tin

Proportion of chocolate in biscuit tin = 10 / [10 + 4]

Proportion of chocolate in biscuit tin = 10 / 14

Proportion of chocolate in biscuit tin = 5:7

Find the following
[tex]2x + 3y = 13[/tex]
[tex]xy = 6[/tex]
find
[tex]8 {x}^{3} + 27 {y}^{3} [/tex]

Answers

Answer:

793

Step-by-step explanation:

x=2, y =3

8x³+27y³ = 64 + 729 = 793

This is for the first one

Solve for X enter your answer in the box

Answers

Answer:

x = 6

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

GIVEN :-

AD ║ BCAE = 16 unitsAB = 5x + 2 unitsDE = 12 unitsDC = 24 units

TO FIND :-

Value of x

GENERAL CONCEPT TO BE USED IN THIS QUESTION :-

Basic Proportionality Theorem -

If a line drawn parallel to one side of a triangle and intersects the other two sides at distinct points , it divides the other two sides in equal proportion.

SOLUTION :-

AD is the line drawn parallel to BC and intersects EB & EC at A & D respectively. By using Basic Proportionality Theorem , it can be stated that -

[tex]\frac{AE}{AB} = \frac{DE}{DC}[/tex]

[tex]=> \frac{16}{5x + 2} = \frac{12}{24}[/tex]

[tex]=> \frac{16}{5x + 2} = \frac{1}{2}[/tex]

[tex]=> 5x + 2 = 16 \times 2 = 32[/tex]

[tex]=> 5x = 32 - 2 = 30[/tex]

[tex]=> x = \frac{30}{5} = 6[/tex]

Find the Ares of a semi circle whose radius is 2.4 cm​

Answers

Answer:

Step-by-step explanation:

area of semi circle=πr^2/2

=3.14*(2.4)^2/2

=3.14*5.76/2

=18.0864/2

=9.0432 cm^2

Answer:

72/25 [tex]\pi[/tex] cm² or 9.047786842... cm²

Step-by-step explanation:

Area of whole circle is [tex]\pi r^{2}[/tex]

[tex]\pi[/tex]×2.4² = 144/25[tex]\pi[/tex] cm² or 18.09557368... cm²

Since it is a semi-circle, divide this value by 2 (or multiply by 0.5, either way, your halving it):

144/25[tex]\pi[/tex] ÷ 2 = 72/25 [tex]\pi[/tex] cm² or 9.047786842... cm²

GJ is a midsegment of △HIK. If HI=s–59 and GJ=s–65, what is the value of s?

Answers

Answer:

s = 71

Step-by-step explanation:

Given that GJ is a midsegment of the triangle then it is half the length of the third side, that is

GJ = [tex]\frac{1}{2}[/tex] HI , so

s - 65 = [tex]\frac{1}{2}[/tex] (s - 59) ← multiply both sides by 2 to clear the fraction

2s - 130 = s - 59 ( subtract s from both sides )

s - 130 = - 59 ( add 130 to both sides )

s = 71

HELP NOWhhhhhhhhhhhhhhhhhhhhhhh

Answers

Answer:

r = 1/5

Step-by-step explanation:

Substitute x=15 and y=3 into the equation given.

Transpose so that r = 3/15

Simply 3/15

r = 1/5

Answer:

4.4/22 = .2

r=.2

Step-by-step explanation:

GELPPPPPP
(1) Distributive property
(2) Associative property
(3) Addition property of equality
(4) Division property of equality

Answers

Distributive property

Help on this anyone?

Answers

Answer:

If angle LMN is 63 degrees and angle LMO is 32 degrees and angle OMN + angle LMO is 63 degrees

we subtract 32 from 63 to find OMN

63-32 = 31

Step-by-step explanation:

Answer:

31 degrees

Step-by-step explanation:

The biggest angle is 63 degrees, for find OMN we have to do

63 - 32 = 31 degrees

Amy deposits $8000 into an account that pays simple interest at a rate of 2% per year how much interest will she be paid in the first 4 years?

Answers

Dona will be paid 80 as interest. https://socratic.org/questions/donna-deposits-s800-into-an-account-that-pays-simple-interest-at-a-rate-of-2-per

What is the area of this cube 6 4 5

Answers

120

6 times 4 times 5 = 120

Hope this helps

PLEASE HELP I'LL GIVE BRAINLIEST

Answers

Answer:

841.8

Step-by-step explanation:

2. Which trinomial below is equivalent to the square of the binomial x-5?
(1) x² + 25
(3) x? - 25
(2) x² -10x+25
(4) x?-10x – 25

Answers

Answer:

2)   x² - 10x + 25

Step-by-step explanation:

(x - 5)(x - 5) = x² - 5x  -5x + 25

Combining like terms

x² - 10x + 25

Robert has 3.38 pounds of cat food he uses 0.26 of cat food to feed one cat how many cats can Robert feed with the cat food he has

Answers

Answer:

Robert can feed 13 cats.

Step-by-step explanation:

To solve this we simply divide.

3.38 divided by 0.26 = 13

Therefore Robert can feed 13 cats.

If f(1)=7 and f(n)=3f(n-1)+3 then find the value of (3)

Answers

Given:

[tex]f(1)=7[/tex]

[tex]f(n)=3f(n-1)+3[/tex]

To find:

The value of f(3).

Solution:

We have,

[tex]f(n)=3f(n-1)+3[/tex]               ...(i)

Substituting [tex]n=2[/tex] in (i), we get

[tex]f(2)=3f(2-1)+3[/tex]

[tex]f(2)=3f(1)+3[/tex]

Substituting [tex]f(1)=7[/tex] in the above equation, we get

[tex]f(2)=3(7)+3[/tex]

[tex]f(2)=21+3[/tex]

[tex]f(2)=24[/tex]

Now, substituting [tex]n=3[/tex] in (i), we get

[tex]f(3)=3f(3-1)+3[/tex]

[tex]f(3)=3f(2)+3[/tex]

Substituting [tex]f(2)=24[/tex] in the above equation, we get

[tex]f(3)=3(24)+3[/tex]

[tex]f(3)=72+3[/tex]

[tex]f(3)=75[/tex]

Therefore, the value of f(3) is 75.

16. Show your work and check your answer(s).
√2x-1+7=4

Answers

Answer

X=25

Step-by-step explanation:

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