The Population Of A City Is Given By The Formulap T 100000e0 01t Wheretis The Number 2802804

  1. The population of a city is given by the formulaP(t) = 100000e0.01t, wheretis the number of years since 2018 (for this question we ignore the fact that population is usually an integer).

    1. (a) In which year the population will double, i.e. findt*such thatP(t*-1)

    2. (b) What will be the population growthP(t*)-P(t*-1) during the yeart*?[1]

    3. (c) Compute the derivativeP'(t) and estimate the valueP'(t*).[1]

    4. (d) Your answers to the previous two parts of this question should be close to each other but not exactly equal. Explain why this might be expected.[2]

    5. (e) Compute the second derivativeP”(t). What property ofP(t) could you use to predict whether
      the answer to part (b) will be higher or lower than the answer to (c)?[2]

Prof. Angela


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