Which statement best describes what happened when h is changed from 4 to

An experiment starts and the population of a bacteria culture increases by 10% in the first hour. Assume that the population inc

Ne4ueva [31]

Answer:

a) The doubling time is 7.27 hours.

b) The population is 6 hours will be 3,543.

Step-by-step explanation:

The population of the bacteria is modeled by the following equation:

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

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

An experiment starts and the population of a bacteria culture increases by 10% in the first hour.

This means that

$P(1) = 1.1P(0)$

Which helps us find r.

So

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

$1.1P(0) = P(0)e^{r}$

$e^{r} = 1.1$

Applying ln to both sides

$\ln{e^{r}} = \ln{1.1}$

$r = 0.0953$

So

$P(t) = P(0)e^{0.0953t}$

a) What is the doubling time?

This is t when $P(t) = 2P(0)$

So

$P(t) = P(0)e^{0.0953t}$

$2P(0) = P(0)e^{0.0953t}$

$e^{0.0953t} = 2$

Applying ln to both sides

$\ln{e^{0.0953t}} = \ln{2}$

$0.0953t = \ln{2}$

$t = \frac{\ln{2}}{0.0953}$

$t = 7.27$

The doubling time is 7.27 hours.

b) If the initial population is 2,000, what is the population in 6 hours?

This is P(6) when $P(0) = 2000$ . So

$P(t) = P(0)e^{0.0953t}$

$P(6) = 2000e^{0.0953*6} = 3543$

The population is 6 hours will be 3,543.

3 0

4 years ago

A number between 1 and 20 that has exactly 5 factors

Allisa [31]

16.
Hope this helps! :)

4 0

4 years ago

Change each standard form equation to slope-intercept form!

goldenfox [79]

Hello!

Slope-intercept form is this one: $y=a*x+b$ where a is the slope and b the intercept.

So, for transforming these equations to Slope-Intercept you'll need to rearrange the equations by adding or subtracting the same amounts on both sides of the equation (as a rule of thumb, sums are transformed into subtractions and multiplications into divisions).

1) 3x + y = 12

You should notice that Y and X are on the same side of the equation, so by subtracting 3x on both sides of the equation you'll cancel X on the left side:

 $3x+y-3x=12-3x \\ y=12-3x$

To finish, we rearrange this equation to the form y=a*x+b

 $y=-3x+12$

So, the slope is -3 and the intercept is 12

2) 8=y+5x

You should notice that Y and X are on the same side of the equation, so by subtracting 5x on both sides of the equation you'll cancel X on the right side:

$8-5x=y+5x-5x \\ 8-5x=y$

To finish, we rearrange this equation to the form y=a*x+b

$y=-5x+8$

So, the slope is -5 and the intercept is 8

3) 6x + 3y = -9

You should notice that Y and X are on the same side of the equation, so by subtracting 6x on both sides of the equation you'll cancel X on the left side:

$6x+3y-6x=-9-6x \\ 3y=-9-6x$

Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by 3 to cancel this number on the left side.

$\frac{3}{3}y= \frac{9}{3}- \frac{6}{3}x \\ y=3-2x$

To finish, we rearrange this equation to the form y=a*x+b

$y=-2x+3$

So, the slope is -2 and the intercept is 3

4) x - 5y = 55

You should notice that Y and X are on the same side of the equation, so by subtracting x on both sides of the equation you'll cancel X on the left side:

$x-5y-x=-55-x \\ -5y=-55-x$

Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by -5 to cancel this number on the left side.

$\frac{-5}{-5}y= \frac{55}{-5}- \frac{1}{-5}x \\ y=-11+ \frac{1}{5}x$

To finish, we rearrange this equation to the form y=a*x+b

$y=\frac{1}{5}x-11$

So, the slope is 1/5 and the intercept is -11

5) -4x-y=-2
You should notice that Y and X are on the same side of the equation, so by adding 4x on both sides of the equation you'll cancel X on the left side:

$-4x-y+4x=-2+4x \\ -y=2+4x$

Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by -1 to cancel this number on the left side.

$\frac{-1}{-1} y= \frac{-2}{-1}+ \frac{4}{-1}x \\ y=2-4x$

To finish, we rearrange this equation to the form y=a*x+b

$y=-4x+2$

So, the slope is -4 and the intercept is 2

6) -16 = -4x + 2y

You should notice that Y and X are on the same side of the equation, so by adding 4x on both sides of the equation you'll cancel X on the right side:

$-16+4x=-4x+2y+4x \\ -16+4x=2y$

Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by 2 to cancel this number on the right side.

$\frac{-16}{2}+ \frac{4}{2} x= \frac{2}{2}y \\ -8+2x=y$

To finish, we rearrange this equation to the form y=a*x+b

$y=2x-8$

So, the slope is 2 and the intercept is -8

I hope that this helps. Have a nice day!

8 0

4 years ago

Please help: what is 262.3 out of 329 as a percent?

zhenek [66]

Answer:

79.72644377% is the answer I believe.

4 0

3 years ago

Read 2 more answers

It’d be a great help if someone could help me with the 4 practice problems (-,b,c & d)

natima [27]

Answer:

idk thats tough

Step-by-step explanation:

4 0

3 years ago

Which statement best describes what happened when h is changed from 4 to - 2.