Ask question

Ask question

All categories

3 years ago

8

The current population of a small town is 2463 people. It is believed that town's population is tripling every 12 years. Approxi

mate the population of the town 5 years from now.
________ residents (round to nearest whole number)

1 answer:

Bingel [31]3 years ago

4 0

{Answer:

3893 residents.

Step-by-step explanation:

Equation for population growth:

The equation for the size of a population, considering that it doubles every n years, is given by:

$A(t) = A(0)(3)^{(\frac{t}{n})}$

In which A(0) is the initial population.

The current population of a small town is 2463 people. It is believed that town's population is tripling every 12 years.

This means that $A(0) = 2463, n = 12$ . So

$A(t) = A(0)(3)^{(\frac{t}{n})}$

$A(t) = 2463(3)^{(\frac{t}{12})}$

Approximate the population of the town 5 years from now.

This is A(5). So

$A(t) = 2463(3)^{(\frac{t}{12})}$

$A(5) = 2463(3)^{(\frac{5}{12})} = 3892.8$

Rounding to the nearest whole number, 3893 residents.

You might be interested in

Please help me with these questions! I have to show work and complete all of this but I'm confused. It is due at 11:59 please he

worty [1.4K]

The answer is in the image. Good luck!

7 0

3 years ago

Read 2 more answers

Find the exact value of each trigonometric function for the given angle θ.

Kay [80]

Answer:

$\sin (240^\circ)=-\dfrac{\sqrt{3}}{2},\cos (240^\circ)=-\dfrac{1}{2},\tan (240^\circ)=\sqrt{3},\cot (240^\circ)=\dfrac{1}{\sqrt{3}},\sec (240^\circ)=-2,\csc (240^\circ)=\dfrac{2}{\sqrt{3}}.$

Step-by-step explanation:

The given angle is 240 degrees.

We need to find the exact value of each trigonometric function for the given angle θ.

Since $\theta=240$ , it means θ lies in 3rd quadrant. In 3d quadrant only tan and cot are positive.

$\sin (240^\circ)=\sin (180^\circ+60^\circ)=-\sin (60^\circ)=-\dfrac{\sqrt{3}}{2}$

$\cos (240^\circ)=\cos (180^\circ+60^\circ)=-\cos (60^\circ)=-\dfrac{1}{2}$

$\tan (240^\circ)=\tan (180^\circ+60^\circ)=\tan (60^\circ)=\sqrt{3}$

$\cot (240^\circ)=\cot (180^\circ+60^\circ)=\cot (60^\circ)=\dfrac{1}{\sqrt{3}}$

$\sec (240^\circ)=\sec (180^\circ+60^\circ)=-\sec (60^\circ)=-2$

$\csc (240^\circ)=\csc (180^\circ+60^\circ)=-\csc (60^\circ)=-\dfrac{2}{\sqrt{3}}$

Therefore, $\sin (240^\circ)=-\dfrac{\sqrt{3}}{2},\cos (240^\circ)=-\dfrac{1}{2},\tan (240^\circ)=\sqrt{3},\cot (240^\circ)=\dfrac{1}{\sqrt{3}},\sec (240^\circ)=-2,\csc (240^\circ)=-\dfrac{2}{\sqrt{3}}.$

8 0

3 years ago

A flag measures 150 feet by 75 feet. Find its area

Mazyrski [523]

Area = length x width

Area = 150 x 75

Area = 11,250 square feet

3 0

3 years ago

Read 2 more answers

Find the vertical and horizontal asymptotes, domain, range, and roots of f (x) = -1 / x-3 +2.

gladu [14]

Answer:

Vertical asymptote: $x=3$

Horizontal asymptote: $f(x) =2$

Domain of f(x) is all real numbers except 3.

Range of f(x) is all real numbers except 2.

Step-by-step explanation:

Given:

Function:

$f (x) = -\dfrac{1 }{ x-3} +2$

One root, $x = 3.5$

To find:

Vertical and horizontal asymptote, domain, range and roots of f(x).

Solution:

First of all, let us find the roots of f(x).

<em>Roots of f(x) means the value of x where f(x) = 0</em>

$0= -\dfrac{1 }{ x-3} +2\\\Rightarrow 2= \dfrac{1 }{ x-3}\\\Rightarrow 2x-2 \times 3=1\\\Rightarrow 2x=7\\\Rightarrow x = 3.5$

One root, $x = 3.5$

Domain of f(x) i.e. the values that we give as input to the function and there is a value of f(x) defined for it.

For x = 3, the value of f(x) $\rightarrow \infty$

For all, other values of $x$ , $f(x)$ is defined.

Hence, Domain of f(x) is all real numbers except 3.

Range of f(x) i.e. the values that are possible output of the function.

f(x) = 2 is not possible in this case because something is subtracted from 2. That something is $\frac{1}{x-3}$ .

Hence, Range of f(x) is all real numbers except 2.

Vertical Asymptote is the value of x, where value of f(x) $\rightarrow \infty$ .

$-\dfrac{1 }{ x-3} +2 \rightarrow \infty$

It is possible only when

$x-3=0\\\Rightarrow x=3$

$\therefore$ vertical asymptote: $x=3$

Horizontal Asymptote is the value of f(x) , where value of x $\rightarrow \infty$ .

$x\rightarrow \infty \Rightarrow \dfrac{1 }{ x-3} \rightarrow 0\\\therefore f(x) =-0+2 \\\Rightarrow f(x) =2$

$\therefore$ Horizontal asymptote: $f(x) =2$

Please refer to the graph of given function as shown in the attached image.

5 0

3 years ago

Simplify the given equation. 5x + 2(x - 3) = -2(x - 1)

svp [43]

On the left side, distribute the 2 to x and -3 so the left side should look like 5x+2x-6.

on the right, distribute the -2 to x and -1 so the right side should look like -2x+2.

combine like terms on the left to get 7x-6=-2x+2

add -2x from the right side to the left side to make the equation 9x-6=2 now it's a two step equation.
add 6 to 2 to get 9x=8. divide by 9 and x=8/9.

8 0

3 years ago