1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
alexdok [17]
3 years ago
8

The number of bacteria after t hours is given by N(t)=250 e^0.15t a) Find the initial number of bacteria and the rate of growth

or decay. b) Find the number of bacteria after 2 days c) How many hours will it take for the number of bacteria to reach 4000? d) How long will it take for the number of bacteria to triple?
Mathematics
1 answer:
Art [367]3 years ago
6 0

Answer:

a) N_0=250\; k=0.15

b) 334,858 bacteria

c) 4.67 hours

d) 2 hours

Step-by-step explanation:

a) Initial number of bacteria is the coefficient, that is, 250. And the growth rate is the coefficient besides “t”: 0.15. It’s rate of growth because of its positive sign; when it’s negative, it’s taken as rate of decay.

Another way to see that is the following:

Initial number of bacteria is N(0), which implies t=0. And N(0)=N_0. The process is:

N(t)=250 e^{0.15t}\\N(0)=250 e^{0.15(0)}\\ N_0=250e^{0}\\N_0=250\cdot1\\ N_0=250

b) After 2 days means t=48. So, we just replace and operate:

N(t)=250 e^{0.15t}\\N(48)=250 e^{0.15(48)}\\ N(48)=250e^{7.2}\\N(48)=334,858\;\text{bacteria}

c) N(t_1)=4000; \;t_1=?

N(t)=250 e^{0.15t}\\4000=250 e^{0.15t_1}\\ \dfrac{4000}{250}= e^{0.15t_1}\\16= e^{0.15t_1}\\ \ln{16}= \ln{e^{0.15t_1}} \\  \ln{16}=0.15t_1 \\ \dfrac{\ln{16}}{0.15}=t_1=4.67\approx 5\;h

d) t_2=?\; (N_0→3N_0 \Longrightarrow 250 → 3\cdot250 =750)

N(t)=250 e^{0.15t}\\ 750=250 e^{0.15t_2} \\ \ln{3} =\ln{e^{0.15t_2}}\\ t_2=\dfrac{\ln{3}}{0.15} = 2.99 \approx 3\;h

You might be interested in
Simplify each of the following logarithmic expressions to the simplest form
AleksAgata [21]
Simplest Form: log2 (x/9)
4 0
3 years ago
Find the distance between the two points.
marusya05 [52]

Answer:

Step-by-step explanation:

8 0
3 years ago
Simplify: <br> (sq root of) a^2 if a&gt;0<br><br> (sq root of) 36x^2 if x≤0
tresset_1 [31]

Answer:


Step-by-step explanation:

1.  (sq root of) a^2 if a>0 => √(a^2) = ±a

2.  (sq root of) 36x^2 if a>0 => ±6x

7 0
3 years ago
What is the distance between the points (7, 8) and (-8, 0) on a coordinate grid
enot [183]

Answer:

the distance is 17

5 0
3 years ago
Read 2 more answers
Angela drew 9 rhombuses and 6 trapezoids. She wants to find q, the total number of angles in her quadrilaterals. Explain how Ang
Reil [10]
Both rhombuses and trapezoids have 4 angles. Angela can add 9 and 6 which will give her 15 and multiply by 4 which will give her 60.

Angela has 60 angles.

I hope this helped!!! :)
5 0
3 years ago
Other questions:
  • Will give brainiest :)
    12·1 answer
  • An artist can paint 4paintings 2 hours what is the artists unit rate
    13·2 answers
  • The point-slope form of the equation of the line that passes through (–4, –3) and (12, 1) is y – 1 = (x – 12). What is the stand
    6·1 answer
  • Please help me! I do not understand how to do this.
    8·1 answer
  • I need dis problem solved
    7·1 answer
  • Some one Please HELP!!!! I WILL VOTE BRAINLIEST ANSWER!!
    14·1 answer
  • The equation of a circle is x2 + y2 =49 . What is the standard form of an equation of the circle after its center is translated
    14·1 answer
  • Khloe drove 204 miles in 4 hours. If she continued at the same rate, how long would
    15·2 answers
  • Molly had 8 apples jim has 8 how many do they have all together
    10·2 answers
  • Using the order of operations, which operation in the expression 3x2-2³÷4 should be completed first
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!