Consider the first four terms of the sequence below.

A bacteria population experiences continuous growth. If there were 2,000 bacteria present at the start of an experiment, how lon

allochka39001 [22]

Answer:

D. About 15.69 hours.

Step-by-step explanation:

Let x be the number of hours.

We have been given that there were 2,000 bacteria present at the start of an experiment and the growth rate was 7% per hour.

Since number of bacteria is growing exponentially, so we will use exponential growth function to solve our given problem.

The continuous exponential growth formula is in form: $y=e^{kx}$ , where,

e= mathematical constant,

k = Growth rate in decimal form.

Let us convert our given rate in decimal form.

$7\%=\frac{7}{100}=0.07$

Upon substituting our given values we will get exponential function for bacteria growth as: $y=2,000*e^{0.07x}$ , where, y represents number of bacteria after x hours.

Since we need to figure out the number of hours it will take for there to be 6,000 bacteria, so we will substitute y= 6,000 in our function.

$6,000=2,000*e^{0.07x}$

Let us divide both sides of our equation by 2,000.

$\frac{6,000}{2,000}=\frac{2,000*e^{0.07x}}{2,000}$

$3=e^{0.07x}$

Let us take natural log of both sides of our equation.

$\text{ln}(3)=ln(e^{0.07x})$

$\text{ln}(3)=0.07x$

$1.0986122=0.07x$

$x=\frac{1.0986122}{0.07}$

$x=15.69446\approx 15.69$

Therefore, it will take about 15.69 hours to be 6,000 bacteria and option D is the correct choice.

3 0

3 years ago

A container holds 9 red markers, 13 blue markers, and 17 green markers. You will randomly select two markers without replacement

IRISSAK [1]

Answer:

a.

R-------8/38--------RR

R------9/39--------B-------13/38-------RB

G------17/38--------RG

R-------9/38--------BR

B--------13/39------B-------12/38-------BB

G-------17/38-------BG

R-----9/38--------GR

G---------17/39-------B------13/38-------GB

G------16/38-------GG

b).

9 ways
ways you can select 1 blue are; RB,BR,BG,GB

RB=9/39 × 13/38=3/38

BR= 13/39 × 9/38 =3/38

BG= 13/39 × 17/38=17/114

GB= 17/39 × 13/38=17/114

=3/38 +3/38+17/114+ 17/114 =26/57

Probability of selecting 2 red markers= RR = 9/39 × 8/38 =12/247

Probability of selecting a green marker and then a red marker= GR= 17/39×9/38 =51/494

8 0

4 years ago

Please help me !! I need help ASAP

vlada-n [284]

Answer:

1/5

Step-by-step explanation:

3 0

4 years ago

Solve for x and y<br> 7x - 3y =23<br>2x - 4y = -8<br>

dybincka [34]

$Q. 7x - 3y =23$

$Lets, \: Find \: x :-$

$7x - 3y = 23$

$7x - 3(0) = 23$

$x = 3.286$

$Now, Lets \: find \: y :-$

$7x - 3y = 23$

$7(0) - 3y = 23$

$y \: = -7.667$

3 0

3 years ago

Read 2 more answers

Unit 3 | Lesson 9

Charra [1.4K]

The formula d = rt gives the distance traveled in time t at rate r. A bicyclist rides for 1.5 hours and travels 25 miles.
d= D. 37.5 miles per hour
r= 25
t=1.5
25*1.5
=37.5

D.
37.5 miles per hour

5 0

3 years ago