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    Quantities that could be modelled by exponential growth or decay

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    Select the three options which are NOT examples of quantities that could be modeled by exponential growth or decay.

    Options

    A. The number of students registering for named degress at the Open University, if each year there are 5% more than the previous year.

    B. The world's reserve of a certain mineral, given that 1000 tonnes of the mineral are mined each year

    C. The population of an endangered species which is found each year to be 9/10 of the previous year's population.

    D. The number of bacteria in a test tube if each one divides into two every hour.

    E. The radioactivity of a sample of a substance which has a half-life of 250 years.

    F. The amount of money owing on a loan of £100 if interest is added monthly at a rate of 1% and there are no repayments.

    G. The amount of money owing on a loan of £100 if interest is added monthly at a rate of 1% and there are monthly repayments of £10

    H. The distance from the ground of an object falling under gravity (ignoring air resistance)

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    Solution Preview

    Ans: B, G, H
    Solution:
    A.) Let in 1st year students took the admission : x
    therefore,
    next year no. of students will take the admission = x +5% of x = 1.05x
    next to next year = 1.05*1.05x = (1.05)^2*x
    so, nth year no. of students taking the admission:
    = (1.05)^(n) * x => exponential increment

    B.) let total reserve of minerals = x tonnes
    After one year = x -1000 tonnes
    After two ...

    Solution Summary

    Different situations are examined as to whether they can be modeled for exponential growth or decay. Detailed reasons are provided.

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