Please help me pleaseeeeeee

A sample of bacteria is being eradicated by an experimental procedure. The population is following a pattern of exponential deca

77julia77 [94]

Answer:

There will be 50 bacteria remaining after 28 minutes.

Step-by-step explanation:

The exponential decay equation is

$N=N_0e^{-rt}$

N= Number of bacteria after t minutes.

$N_0$ = Initial number of bacteria when t=0.

r= Rate of decay per minute

t= time is in minute.

The sample begins with 500 bacteria and after 11 minutes there are 200 bacteria.

N=200

$N_0$ = 500

t=11 minutes

r=?

$N=N_0e^{-rt}$

$\therefore 200=500e^{-11r}$

$\Rightarrow e^{-11r}=\frac{200}{500}$

Taking ln both sides

$\Rightarrow ln| e^{-11r}|=ln|\frac{2}{5}|$

$\Rightarrow {-11r}=ln|\frac{2}{5}|$

$\Rightarrow r}=\frac{ln|\frac{2}{5}|}{-11}$

To find the time when there will be 50 bacteria remaining, we plug N=50, $N_0$ = 500 and $r}=\frac{ln|\frac{2}{5}|}{-11}$ in exponential decay equation.

$50=500e^{-\frac{ln|\frac25|}{-11}.t}$

$\Rightarrow \frac{50}{500}=e^{\frac{ln|\frac25|}{11}.t}$

Taking ln both sides

$\Rightarrow ln|\frac{50}{500}|=ln|e^{\frac{ln|\frac25|}{11}.t}|$

$\Rightarrow ln|\frac{1}{10}|={\frac{ln|\frac25|}{11}.t}$

$\Rightarrow t= \frac{ln|\frac{1}{10}|}{\frac{ln|\frac25|}{11}.}$

$\Rightarrow t= \frac{11\times ln|\frac{1}{10}|}{{ln|\frac25|}}$

$\Rightarrow t\approx 28$ minutes

There will be 50 bacteria remaining after 28 minutes.

3 0

3 years ago

The following is a student’s work when solving for y. There is a mistake in the work. What is the mistake? What is the correct a

laila [671]

Answer:

Part 1

The mistake is Step 2: P + 2·x = 2·y

Part 2

The correct answer is

Step 2 correction: P - 2·x = 2·y

(P - 2·x)/2 = y

Step-by-step explanation:

Part 1

The student's steps are;

Step 1; P = 2·x + 2·y

Step 2: P + 2·x = 2·y

Step 3: P + 2·x/2 = y

The mistake in the work is in Step 2

The mistake is moving 2·x to the left hand side of the equation by adding 2·x to <em>P </em>to get; P + 2·x = 2·y

Part 2

To correct method to move 2·x to the left hand side of the equation, leaving only 2·y on the right hand side is to subtract 2·x from both sides of the equation as follows;

Step 2 correction: P - 2·x = 2·x + 2·y - 2·x = 2·x - 2·x + 2·y = 2·y

∴ P - 2·x = 2·y

(P - 2·x)/2 = y

y = (P - 2·x)/2

7 0

2 years ago

Please help me it’s due right now?!?! <br> Find the missing side of each triangle.

Sever21 [200]

Answer:

x = 2√5

Step-by-step explanation:

Using the Pythagorean Theorem: