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The count in a bacteria culture was 100 after 20 minutes and 2000 after 40 minutes. Assuming the count grows exponentially, What

Afina-wow [57]

Answer:

Explanation:

Let X be the number of bacteria at time t, and Xo be the initial number of bacteria

Bacteria grows exponentially, the exponential growth model is thus:

X = Xo $e^{kt}$

[e is the exponential sign]

k is the growth constant = growth rate

At t = 20 minutes, X = 100

At t = 40 minutes, X = 2000

Substituting that into the formula

(i) ... 100 = Xo $e^{k20}$

(ii) ... 2000 = Xo $e^{k40}$

Divide (ii) by (i)

$\frac{2000}{100} = \frac{Xoe^{40k} } {Xoe^{20k}}$

20 = $e^{40k-20k} = e^{20k}$

[Xo cancels Xo. Division of values raised to a power is done by subtracting their powers]

Take the natural log of both sides

㏑20 = 20k

[taking the ㏑ cancels the exponential]

k = $\frac{ln20}{20}$

We can now substitute k to solve one of the equations

substituting k in (ii): 2000 = Xo $e\frac{ln 20}{20}.^{40}$

2000 = Xo $e^{0.15*40}$

2000 = Xo $e^{6}$

Making Xo the subject of the formula

Xo = $\frac{2000}{e^{6} }$

Xo is approximately 5 cells.

THE DOUBLING TIME

The doubling time is the time it takes for the population to double, so 5 cells become 10 cells

Since Xo = 5

Given that X = Xo $e^{kt}$

When X=10,

10 = 5 $e^{0.15t}$

solving for t:

$e^{0.15t} = \frac{10}{5}$

Take ln of both sides

0.15t = ln 2

t = $\frac{ln2}{0.15}$

t =4.62 minutes

POPULATION AFTER 65 MINUTES

X = 5 $e^{0.15*65}$

X = 85770

WHEN WILL THE POPULATION REACH 12000

12000 = 5 $e^{0.15t}$

$e^{0.15t}$ =240

take ln of both sides

0.15t = ln 2400

t = 51.89 minutes (approximately 52 minutes)

6 0

3 years ago

If the kidney cell of a bird has 64 chromosomes how many chromosones does the sperm of this bird have

ioda

Gametes, or sperm and egg cells are both haploid cells, meaning that they have half the amount of chromosomes that regular body cells do, meaning that the sperm cell of this bird would have 32 chromosomes.

4 0

3 years ago

The cartilage on the ends of wendell's joints is deteriorating. around age 65, he developed bony lumps on the end of the joints

vivado [14]

Arthritis is a joint disorder involving joint inflammation.Pain is often localized to only the affected joint. Osteoarthritis is a wear and tear type of arthritis often affects aging population affecting joints in hands,knees and lower back. Heberden's node is an example and develops around middle age thus Wendell might have this.

8 0

4 years ago

Suppose a researcher wants to know whether a high protein diet causes children to learn better in school. half of the children i

denis-greek [22]

the control group would be the children eating their normal diet

8 0

4 years ago

Kris' case is unusual, because parkinson's disease usually takes many decades to kill enough neurons (cells in the brain) to cau

Leto [7]

Answer;

-The neurons would be unable to transport substance between different parts of the cell.

Explanation;

-Neurons are specialized eukaryotic cells that extend long processes to form connections in the nervous system. They have a cytoskeleton that consists of three main polymers: microtubules, intermediate filaments and actin filaments.

-The cytoskeleton is required for axon formation and axonal transport and also provides the structural basis for several specialized axonal structures, such as the axon initial segment and presynaptic boutons.

6 0

4 years ago