In a certain population of microbes in a petri dish, the rate of increase in the population is 9 percent per hour. The time it takes for a given population to double can be estimated using the formula 70/thours, where t is the rate of increase per hour expressed as a percent. If the number of microbes in the dish is 60,000 at the start of the first hour, what will be the approximate number of microbes after 48 hours?a)120,000b)420,000c)720,000d)1,900,000e)3,800,000Correct answer is option 'E'. Can you explain this answer?

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In a certain population of microbes in a petri dish, the rate of increase in the population is 9 percent per hour. The time it takes for a given population to double can be estimated using the formula 70/t hours, where t is the rate of increase per hour expressed as a percent. If the number of microbes in the dish is 60,000 at the start of the first hour, what will be the approximate number of microbes after 48 hours?

a)
120,000
b)
420,000
c)
720,000
d)
1,900,000
e)
3,800,000

Correct answer is option 'E'. Can you explain this answer?

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In a certain population of microbes in a petri dish, the rate of incre...

Given:
- Rate of increase in the population is 9 percent per hour.
- Formula to estimate the time taken for a given population to double: 70/t (hours), where t is the rate of increase per hour expressed as a percent.
- Number of microbes at the start of the first hour is 60,000.

To find:
The approximate number of microbes after 48 hours.

Solution:

Step 1: Calculate the rate of increase per hour:
Given that the rate of increase in the population is 9 percent per hour.

Rate of increase per hour = 9%

Step 2: Calculate the time taken for the population to double:
Using the formula: 70/t (hours), where t is the rate of increase per hour expressed as a percent.

Time taken to double = 70/9

Simplifying, we get:

Time taken to double = 7.78 hours (approximately)

Step 3: Calculate the number of microbes after 48 hours:
Given that the number of microbes at the start of the first hour is 60,000.

Since the population doubles every 7.78 hours, we can calculate the number of doubling intervals in 48 hours:

Number of doubling intervals = 48/7.78

Simplifying, we get:

Number of doubling intervals = 6.17 (approximately)

To find the final number of microbes, we multiply the initial population by 2 for each doubling interval:

Final number of microbes = 60,000 * (2^6.17)

Simplifying, we get:

Final number of microbes = 60,000 * 98.46

Final number of microbes = 5,907,600 (approximately)

Therefore, the approximate number of microbes after 48 hours is 5,907,600, which corresponds to option E.

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In a certain population of microbes in a petri dish, the rate of incre...

To estimate the number of microbes after 48 hours, we can use the formula provided: 70/t hours, where t is the rate of increase per hour expressed as a percent.

Given:
Rate of increase = 9 percent per hour
Number of microbes at the start = 60,000

Using the formula, we can calculate the approximate doubling time:
Doubling time (t) = 70 / 9
Doubling time (t) ≈ 7.78 hours

Now, we can calculate the number of doublings that occur in 48 hours:
Number of doublings = 48 hours / 7.78 hours ≈ 6.16 doublings

Since the population doubles approximately every 7.78 hours, after 6.16 doublings, the population will be approximately 2^6.16 times the initial population.

Approximate number of microbes after 48 hours = 60,000 * 2^6.16 ≈ 3,800,000

Among the answer choices provided, the closest value to the calculated approximate number of microbes is 3,800,000 (option E).

Therefore, the correct answer is E) 3,800,000.

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In a certain population of microbes in a petri dish, the rate of increase in the population is 9 percent per hour. The time it takes for a given population to double can be estimated using the formula 70/thours, where t is the rate of increase per hour expressed as a percent. If the number of microbes in the dish is 60,000 at the start of the first hour, what will be the approximate number of microbes after 48 hours?a)120,000b)420,000c)720,000d)1,900,000e)3,800,000Correct answer is option 'E'. Can you explain this answer?

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