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Julli [10]
3 years ago
15

Evaluate the equation.

Mathematics
1 answer:
e-lub [12.9K]3 years ago
5 0

Answer:

a = 6

Step-by-step explanation:

subtract 6.6 from both sides and you get the answer

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MCR3U1 Culminating 2021.pdf
11111nata11111 [884]

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.

8 0
2 years ago
What adds to -9, and multiplies to -70?
dybincka [34]
-14 and 5 (-14+5 = -9) and -14*5) = -70

Make me the brainliest answer.
4 0
3 years ago
4x + 5 + 5x + 6 = 29. Whats X?
BigorU [14]

Answer:

9x

Step-by-step explanation:

the full answer is 9x+11=29

3 0
3 years ago
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What is 15+9+20+22+9 then x 5?
AfilCa [17]

Answer: oops 375 idk what happend

Step-by-step explanation:

tysm

6 0
3 years ago
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Sup community simplify this in 5 mins −5·(−a)·(−a)·(−4)·a thx 4 help!!!!1111!!!1!111
liraira [26]

Answer:

20a³

Step-by-step explanation:

Simply multiply:

-5(-4) = 20

-a(-a)(a) = a²(a) = a³

20a³

6 0
2 years ago
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