
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).

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

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

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

(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]

(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]
