he population of a particular town is given by the function P(t) = 1,200(1.05)2t, where t is the time in years and P(t) is the population after t years. What is the current population, the percentage growth rate, and the population size (rounded to the nearest whole person) in 7 years?

Hint: Percentage Growth Rate = r ⋅ 100 in A = A0(1 + r)t (4 points)

1,200, 5% annually, and 1,689
1,200, 50% semiannually, and 20,503
1,200, 10.5% per year, and 2,414
1,200, 5% semiannually, and 2,376

a. By the chain rule,

[tex]\dfrac{dy}{dx} = \dfrac{dy}{dt}\cdot\dfrac{dt}{dx} = \dfrac{dy}{dt}\cdot\dfrac{1}{\frac{dx}{dt}}[/tex]

Given that [tex]y=e^t+e^{-t}[/tex] and [tex]x=e^{-t}[/tex], we have the derivatives

[tex]\dfrac{dy}{dt} = e^t -e^{-t}[/tex]

[tex]\dfrac{dx}{dt} = -e^{-t}[/tex]

and so

[tex]\dfrac{dy}{dx} = \dfrac{e^t - e^{-t}}{-e^{-t}} = 1-e^{2t}[/tex]

Set this equal to zero and solve for t :

[tex]1-e^{2t} = 0[/tex]

[tex]1 = e^{2t}[/tex]

[tex]\ln(1) = \ln\left(e^{2t}\right)[/tex]

[tex]0 = 2t \ln(e)[/tex]

[tex]0 = 2t[/tex]

[tex]t=0[/tex]

This value of t corresponds to x = e⁰ = 1 and y = e⁰ - 1/e⁰ = 1 - 1 = 0. So the only point on the curve where the derivative dy/dx is zero is (1, 0).

b. Compute the second derivative. Since dy/dx is a function of t, we'll momentarily replace it with f(t). By the chain rule,

[tex]\dfrac{d^2}{dx^2} = \dfrac d{dx} \dfrac{dy}{dx} = \dfrac{df}{dx} = \dfrac{df}{dt}\cdot\dfrac{dt}{dx} = \dfrac{df}{dt}\cdot\dfrac{1}{\frac{dx}{dt}}[/tex]

We have

[tex]\dfrac{df}{dt} = -2e^{2t}[/tex]

and we've already committed dx/dt. So

[tex]\dfrac{d^2}{dx^2} = \dfrac{-2e^{2t}}{-e^{-t}} = 2e^{3t} [/tex]

Substitute the first and second derivative into the differential equation:

[tex]\left(\dfrac{d^2y}{dx^2}\right)^2 + \dfrac{dy}{dx} - 1 = 0[/tex]

[tex]\left(2e^{3t}\right)^2 + (1-e^{2t}) - 1 = 0[/tex]

[tex]4e^{6t} -e^{2t}= 0[/tex]

[tex]e^{2t} (4e^{4t} - 1) = 0[/tex]

[tex]4e^{4t} - 1 = 0[/tex]

[tex]4e^{4t} = 1[/tex]

[tex]e^{4t} = \dfrac14[/tex]

[tex]\ln\left(e^{4t}\right) = \ln\left( \dfrac14\right)[/tex]

[tex]4t \ln(e) = -\ln(4)[/tex]

[tex]4t = -\ln(4)[/tex]

[tex]t = -\dfrac{\ln(4)}4[/tex]

Answer: Yes

Step-by-step explanation: They are similar because it the same kind of triangle just ones smaller and the other is bigger.

Answer:

A. 20

Step-by-step explanation:

1. To solve this problem, instead of doing 80/100 times 16, we can do 100/80 times 16 (inverse of percentage, basically).

Therefore, the answer is A. 20.

Answer:

On the number line, a number and its opposite are, predictably, opposite each other. In other words, they are the same distance from zero, but on opposite sides of the number line. The opposite of zero is defined to be simply zero. The sum of a number and its opposite is always zero, as shown in the following example.

Answer:

C

Step-by-step explanation:

because i said

mx + 5 = (x - 5) / m

mx + 5 = x/m - 5/mAnswer:

Step-by-step explanation:

first find the inverse equation

y = mx + 5

y - 5 = mx

(y - 5) / m = x

(x - 5) / m = f⁻ˣ(x)

The original function is a line with slope m and y intercept of 5

The inverse function is a line with a slope 1/m and x intercept of 5

so the common line is where m = 1/m

m = 1/m

m² = 1

m = ± 1

The only line with a common slope between these two options is when

m = -1 and y intercept is 5

Answer:

Find out the value of x.

To prove

Definition of mid- segment

It is a segment connecting the midpoints of two sides of a triangle.

It is always parallel to the third side, and the length of the midsegment is half the length of the third side.

As shown in the triangle given below.

As given

DE = 5x and BC = 11x – 15

Thus

15 = 11x - 10x

15 = x

Therefore the value of x is 15 .

Step-by-step explanation:

Answer:

Step-by-step explanation:

1

Answer:

Step-by-step explanation:

Answer:

14/4

Step-by-step explanation:

speed.time=distance

3x4.8=14.4

Answer:

.923

Step-by-step explanation:

1.3 X 0.71 = .923

:))

[tex] \: \: \: \: \: \: [/tex]

[tex] = 3a ^{4} \times (7 {a}^{5} - 2)[/tex]

Step-by-step explanation:

[tex]21 {a}^{9} - 6 {a}^{4} [/tex]

[tex] = 3 {a}^{4} \times (7 {a}^{5} - 2)[/tex]

[tex] \: \: \: \: \: \: [/tex]

Based on the information given the percent of the total cost of the bike has Wu saved is 30%.

Using this formula

Total cost percentage=Amount saved/Cost×100

Where:

Amount saved=$75

Cost =$250

Let plug in the formula

Total cost percentage=$75/$250×100

Total cost percentage=30%

Inconclusion the percent of the total cost of the bike has Wu saved is 30%.

Learn more here:

https://brainly.com/question/17157877

Answer:

Neither.

Step-by-step explanation:

Manipulate the formulas into slope-intercept form which is [tex]y=mx+b[/tex].

In order for them to be parallel, m needs to be the same. Perpendicular, m for one needs to be the negative reciprocal of the other [tex]m=-\frac{1}{m}[/tex].

Let's see what we get.

(1)

[tex]3x+4y=2\\4y=-3x+2\\y=-\frac{3}{4}x+1/2[/tex]

(2)

[tex]4x+3y=2\\3y=-4x+2\\y=-\frac{4}{3}x+2/3[/tex]

They are reciprocals, but they are both negative. So, they are not the same line, perpendicular, nor parallel.

Also, you can graph these equations on desmos and see easily that they have none of these relationships.

Answer:479001600

Step-by-step explanation:

12 factorial is 12 * 11 * 10 ..... all the way to one

A way to do it by hand is

12 * 1

11 * 2

10 * 3

9 * 4

8 * 5

7 * 6

stop here because 6 * 7 and 5 *8 are already listed

This gives you 6 products then multiply those 6 products by pairs which gives you three pairs which gives you three products then compute a pair then multiply by last product.

Easy math but a lot of written work

9514 1404 393

Answer:

  (c)  ΔTRS

Step-by-step explanation:

Perhaps the easiest way to find corresponding vertices is to look at the angle markings:

  1 mark: angles J and T

  2 marks: angles K and R

  3 marks: angles I and S

Then, in order of corresponding angles, we have ...

  ΔJKI ≅ ΔTRS

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

The problem [tex]2x - 3x = 3[/tex] is incorrect. The correct answer for that one is [tex]-x \:\sf{or\:-1[/tex]

[tex]\sf{Simplify\: the\: expression.[/tex]

[tex]\sf{\frac{16x}{64x} = \frac{1}{4}[/tex]

[tex]x=\frac{1}{4}[/tex]

Therefore, the answer is [tex]\frac{1}{4}[/tex]

Answer:

-3 - (2w)

Step-by-step explanation:

hope this helps!

9514 1404 393

Answer:

  (c) 5y - x = -20

Step-by-step explanation:

When the x- and y-terms are on the same side of the equation, the slope of the line will be ...

  m = -(coefficient of x)/(coefficient of y)

So, the slopes of the offered choices are ...

  a) -5/1 = -5

  b) -1/5

 c) -(-1)/5 = 1/5 . . . . . parallel to given line

  d) -5/-1 = 5

The lines will be parallel when their slopes are the same. The slope of the given line is the coefficient of x, 1/5. Choice C has the same slope.

Answer:

9/2

Step-by-step explanation:

m=∆y/∆x

m= (5+4)/(2—0)

m=9/2

Answer: answer is C

Step-by-step explanation:

Answer:

i think it is :

5×5×5=125

2×2×2=8

Answer:

3:4 itself.

3:4 itself.

Step-by-step explanation:

3:4 itself.

Answer:

625.25

Step-by-step explanation:

the answer is 625.25

Answer: 625.25

Step-by-step explanation:

Answer:

y = 5 x + 7

Step-by-step explanation:

Answer:

(1, -4)

Step-by-step explanation:

(-5,-4) -> (x,y) so x = -5 and y = -4. Apply the rule (x+6,y) to that point by substituting in your x and y values.

(-5+6,-4) = (1, -4)

Answer:

10.4

Step-by-step explanation:

x=3⇒f(3)= 4×3+3=15

x=3⇒g(3)=8/3+2≈4.6

f(3)-g(3)=15-4.6=10.4