PLEASE HELP

The population of a community is known to increase at a rate proportional to the number of people present at time t. If the popu

Lady bird [3.3K]

Answer:

$P(t) = P(0)e^{0.0693t}$

Step-by-step explanation:

The population of a community is known to increase at a rate proportional to the number of people present at time t.

This means that the population growth is modeled by the following differential equation:

$\frac{dP(t)}{dt} = rP(t)$

Which has the following solution:

$P(t) = P(0)e^{rt}$

In which P(t) is the population after t years, P(0) is the initial population and r is the growth rate.

The population has doubled in 10 years

This means that $P(10) = 2P(0)$ . We use this to find r.

$P(t) = P(0)e^{rt}$

$2P(0) = P(0)e^{10r}$

$e^{10r} = 2$

$\ln{e^{10r}} = \ln{2}$

$10r = \ln{2}$

$r = \frac{\ln{2}}{10}$

$r = 0.0693$

So the equation that will estimate the population of the community in t years is:

$P(t) = P(0)e^{0.0693t}$

6 0

3 years ago

Solve with cramer's rule x+2y+3z=11, 2x+y+2z=10, 3x+2y+z=9

nalin [4]

Answer:

x = 2 , y = 0 , z = 3

Step-by-step explanation:

Cramer's rule is a rule through which we can find the solution of linear equation.

we have the three linear equations as

x+2y+3z=11

2x+y+2z=10

3x+2y+z=9

AX=B

A: coefficient matrix

X= unknown vectors(x,y,z)

D = values of the linear equation (11 , 10 , 9)

now we find the determinant of the given linear equation

determinant of the matrix will be

A = $\left[\begin{array}{ccc}1&2&3\\2&1&2\\3&2&1\end{array}\right]$ = 1(1-4) - 2(2-6) + 3(4 - 3)

= 1(-3) - 2(-4) + 3(1)

= -3+8+3 = 8

also D $\neq 0$

so the determinant is Non zero we can apply Cramer's rule

we will be replacing the first column of the coefficient matrix A with the values of D

by replacing the first column we will get the value of the variable 'x'

Dx = $\left[\begin{array}{ccc}11&2&3\\10&1&2\\9&2&1\end{array}\right]$ = 11(1-4) -2(10-18) + 3(20-9) = -33+16+33 = 16

x = $\frac{Dx}{D}$ = $\frac{16}{8}$ = 2

similarly

Dy = $\left[\begin{array}{ccc}1&11&3\\2&10&2\\3&9&1\end{array}\right]$ = 1(10-18) -11(2-6) + 3(18 -30) = -8 +44 -36 = 0

y = $\frac{Dy}{D}$ = 0

Dz= $\left[\begin{array}{ccc}1&2&11\\2&1&10\\3&2&9\end{array}\right]$ = 1(9 - 20) -2(18 - 30) + 11(4 -3) = -11 +24 +11 = 24

z = $\frac{Dz}{D}$ = $\frac{24}{8} = 3$

so we have the solution as

x = 2 , y = 0 , z = 3

Therefore the solution for the given linear equations is (2,0,3).

3 0

3 years ago

a circle has a radius of 9 inches. In inches, what is the length of the arc intercepted by central angle of 3.25 radians

frutty [35]

Answer:

$\boxed {\boxed {\sf 29.25 \ inches}}$

Step-by-step explanation:

Since we are given the central angle in radians, we should use the following formula for the arc length.

$s= \theta r$

Where s is the arc length, θ is the angle in radians, and r is the radius.

We know this circle has a radius of 9 inches and the central angle is 3.25 radians.

θ= 3.25
r= 9 in

Substitute the values into the formula

$s= (3.25)( 9 \ in)$

Multiply.

$s= 29.25 \ in$

The arc length is 29.25 inches.

3 0

3 years ago

Chelsea made 15 of the 28 recipes she downloaded from the Internet. What percent of the recipes did she make?

Elanso [62]

Hello there!

28 recipes .......> 100%
15 recipes .......> x%

Cross multiply
28x = 15*100
28x = 1500
x= 1500/28
x ≈ 53.5%

She makes 53.5% of the recipes.

I hope that helps!

5 0

3 years ago

There are 4000 books in the towns library. Of these 2600 are fiction percent equation

iVinArrow [24]

% = 2600/4000 = 0.65 = 65% fiction

7 0

3 years ago