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
kompoz [17]
3 years ago
13

MCR3U1 Culminating 2021.pdf

Mathematics
1 answer:
11111nata11111 [884]3 years ago
8 0

Answer:

(a) y = 350,000 \times (1 + 0.07132)^t

(b) (i) The population after 8 hours is 607,325

(ii) The population after 24 hours is 1,828,643

(c) The rate of increase of the population as a percentage per hour is 7.132%

(d) The doubling time of the population is approximately, 10.06 hours

Step-by-step explanation:

(a) The initial population of the bacteria, y₁ = a = 350,000

The time the colony grows, t = 12 hours

The final population of bacteria in the colony, y₂ = 800,000

The exponential growth model, can be written as follows;

y = a \cdot (1 + r)^t

Plugging in the values, we get;

800,000 = 350,000 \times (1 + r)^{12}

Therefore;

(1 + r)¹² = 800,000/350,000 = 16/7

12·㏑(1 + r) = ㏑(16/7)

㏑(1 + r) = (㏑(16/7))/12

r = e^((㏑(16/7))/12) - 1 ≈ 0.07132

The  model is therefore;

y = 350,000 \times (1 + 0.07132)^t

(b) (i) The population after 8 hours is given as follows;

y = 350,000 × (1 + 0.07132)⁸ ≈ 607,325.82

By rounding down, we have;

The population after 8 hours, y = 607,325

(ii) The population after 24 hours is given as follows;

y = 350,000 × (1 + 0.07132)²⁴ ≈ 1,828,643.92571

By rounding down, we have;

The population after 24 hours, y = 1,828,643

(c) The rate of increase of the population as a percentage per hour =  r × 100

∴   The rate of increase of the population as a percentage = 0.07132 × 100 = 7.132%

(d) The doubling time of the population is the time it takes the population to double, which is given as follows;

Initial population = y

Final population = 2·y

The doubling time of the population is therefore;

2 \cdot y = y \times (1 + 0.07132)^t

Therefore, we have;

2·y/y =2 = (1 + 0.07132)^t

t = ln2/(ln(1 + 0.07132)) ≈ 10.06

The doubling time of the population is approximately, 10.06 hours.

You might be interested in
What's the answer to tripling the greater of the two consecutive even integers gives the same result as subtracting 10 from the
Ostrovityanka [42]

let the 2 integers be x and x + 2.

so we have the equation:-

3(x + 2)  = x - 10

3x + 6 = x - 10

2x = -16

x = -8

the integers are -8 and -6  answer


5 0
3 years ago
What is the slope in the equation: y=4x+3
kompoz [17]

Answer:

The slope is −4 . The equation is in slope-intercept form, y=mx+c , where m is the

Step-by-step explanation:

thanks me

7 0
3 years ago
Simplify ........ (256y²⁵⁶) ⅛<br>help asap!!!!!​
AVprozaik [17]

Answer:

2y^32

Step-by-step explanation:

Since 2^8 = 256, the eighth root of 256 is 2.

Next, we find the power of y by multiplying 256 and 1/8:  result is 32.

Complete answer:  2y^32

7 0
3 years ago
The ratio of berries to oranges is 10:1 if there are 25 oranges, how many berries are there?
Kryger [21]

Answer:

250 berries

Step-by-step explanation:

There are 10 berries to every orange there is. It is given that there are 25 oranges. Simply multiply 10 with 25:

10 x 25 = 250

There are 250 berries.

~

3 0
3 years ago
Read 2 more answers
Write an equation for a slope of -2 And y-intercept of 7
larisa86 [58]
Y=-2x+7 That is the equation written in y=mx+b formula

4 0
3 years ago
Read 2 more answers
Other questions:
  • The width of a rectangle is y feet long. The rectangle is 4 feet longer than it is wide. What is the area of the rectangle?
    6·2 answers
  • What fraction of the flag is painted red?
    10·1 answer
  • The length of a poster is 4 feet long how long is the poster in inches
    10·1 answer
  • What is the constant term in the expression 5x2 + 7x + 4?
    7·1 answer
  • Eva was driving down a road and after 4 hours she had traveled 90 miles. At this
    12·1 answer
  • PLEAAAAASE HELP MEEEE​
    5·2 answers
  • Students are planting a flower bed for science class. The flower bed can be 4.5 ft wide and will be divided into 2 sections for
    7·1 answer
  • 2<br> If = 9 and 3p = x, what is the value of 4p?<br> A) 6<br> B) 12<br> C) 18<br> D) 24
    5·1 answer
  • Simplify.<br><br> (–28xy) ÷ (–4)<br><br><br> −7xy <br><br> 17ab <br><br> −17ab <br><br> 7xy
    12·1 answer
  • A T-shirt company charges $4 per T-shirt, plus a
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!