Suppose that a quantity can be described by the exponential growth equation y(t) = y₀e^kt.

(a) Show that the quantity 1/t in (y(t)/y₀) is a constant.

(b) For the shingles data in Exercise 54 of the previous section, reproduced below, let t = 0 correspond to age 7. Calculate the expression in part (a) for the other ages. To what extent is this expression constant?

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Age 7 22 35 45 55 65 75 Cases per 1000 person-years 1.1 1.4 2.0 2.9 4.6 6.9 9.5