The initial circumference is 5.00 m, and after one year it is 5.02 m. We assume the circumferences form a geometric progression.

The common ratio, \(r\), is calculated as:

\(r = \frac{5.02}{5} = 1.004\)

To find the circumference 20 years after the first measurement, we use the formula for the \(n\)-th term of a geometric progression:

\(a_n = a_1 imes r^{n-1}\)

Here, \(a_1 = 5.00\), \(r = 1.004\), and \(n = 21\) (since we want the circumference after 20 years, starting from the first measurement):

\(a_{21} = 5.00 imes (1.004)^{20}\)

Calculating this gives:

\(a_{21} = 5.42\) m