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Papessa [141]
3 years ago
6

What is the slope of the line through (1,-1) and (5,-7)​

Mathematics
1 answer:
Ber [7]3 years ago
7 0

Answer:

-1.5

Step-by-step explanation:

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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
What is the solution to the inequality &gt; 20?<br><br> x 4<br> x 100
professor190 [17]

Answer:

100

Step-by-step explanation:

7 0
3 years ago
PLEASE HELP ME I need it fast don’t explain
Katena32 [7]

Answer:

The answer should be A, I think.

5 0
3 years ago
I really need help!! can u pwease help ;-;
Nata [24]

Answer:

b

Step-by-step explanation:

6 0
3 years ago
£25 in the ratio 2:3
never [62]
2+3=5
25/5=5
5x2=10 3x5=15
so the answer is:
£10:£15
4 0
3 years ago
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