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Growth or decay proportional to the amount present: value or time from two readings

This type of question, asked 11 times: 9 May 2023 S1, 9 May 2023 S2, 11 May 2023 S1, 16 May 2023 S2, 10 May 2024 S2, 12 May 2024 S1, 21 Apr 2025 S2, 22 Apr 2025 S1, 25 Apr 2025 S1, 25 Apr 2025 S2, 26 Apr 2025 S2. All 11 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    9 May 2023 S1

    103
    The population of a town increases at a rate proportional to the population at that time. If the population increases from 40 thousand to 80 thousand in 40 years, then the population in another 40 years will be

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  2. Question 2

    9 May 2023 S2

    145
    In a certain culture of bacteria, the rate of increase is proportional to the number present. If there are 10410^4 at the end of 3 hours and 4⋅1044\cdot10^4 at the end of 5 hours, then there were _____ in the beginning.

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  3. Question 3

    11 May 2023 S1

    113
    The bacteria increase at the rate proportional to the number of bacteria present. If the original number N doubles in 8 hours, then the number of bacteria in 24 hours will be

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  4. Question 4

    16 May 2023 S2

    134
    The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 1000 at t=0t=0. The number of bacteria is increased by 20% in 2 hours. If the population of bacteria is 2000 after klog⁡65\dfrac{k}{\log\frac{6}{5}} hours, then (klog⁡2)2\left(\dfrac{k}{\log 2}\right)^2 is

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  5. Question 5

    10 May 2024 S2

    144
    In a certain culture of bacteria, the rate of increase is proportional to the number of bacteria present at that instant. It is found that there are 10,000 bacteria at the end of 3 hours and 40,000 bacteria at the end of 5 hours, then the number of bacteria present in the beginning are

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  6. Question 6

    12 May 2024 S1

    108
    The decay rate of radioactive material at any time tt is proportional to its mass at that time. The mass is 27 grams when t=0t=0. After three hours it was found that 8 grams are left. Then the substance left after one more hour is

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  7. Question 7

    21 Apr 2025 S2

    150
    In a culture bacteria count is 1,00,0001,00,000 initially. The number increases by 10%10\% in first 2 hours. In how many hours will the count reach 2,00,0002,00,000, if the rate of growth of bacteria is proportional to the number present?

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  8. Question 8

    22 Apr 2025 S1

    123
    The population of a town increases at a rate proportional to the population at that time. If the population increases from forty thousand to eighty thousand in 20 years, then the population in another 40 years will be

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  9. Question 9

    25 Apr 2025 S1

    104
    The rate at which the population of a city increases varies as the population. In a period of 20 years, the population increased from 4 lakhs to 6 lakhs. In another 20 years the population will be

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  10. Question 10

    25 Apr 2025 S2

    111
    The rate of increase of the population of a city is proportional to the population present at that instant. In the period of 40 years the population increased from 30,000 to 40,000. At any time tt the population is (a)(b)t40(a)(b)^{\frac{t}{40}}. Then the values of a and bb are respectively

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  11. Question 11

    26 Apr 2025 S2

    128
    The population of towns A and B increase at the rate proportional to their population present at that time. At the end of the year 1984, the population of both the towns was 20,000. At the end of the year 1989, the population of town A was 25,000 and that of town B was 28,000. The difference of populations of towns A and B at the end of 1994 was

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