The number of members of the Royal Belgian Tennis Association has increased exponentially in the last century.

In the founding year of 1902, there were only 700 members but every year since that time this number has

increased by 1.7%. Consider the time as a continuous variable.

a) Calculate the growth percentage per month of the number of members in this tennis association. Round

to two decimals.

However, the membership fee that members have to pay yearly also increases over the years. At the

establishment, the yearly total revenue that the treasurer of the tennis association receives due to membership

fees (converted into euros) was only € 980 in 1902. This amount has increased by 3.7% every year since the

start. However, the following rule can be found in the statutes: “By a decision of the annual general meeting,

the total revenue will increase by 1.7% when the total revenue exceeds € 200 000.”

b) Assuming that the yearly increase of 3.7% continues in the future, when will the tennis association

intervene in the membership fees such that the total revenue increases by only 1.7% according to the

rule laid down in the statutes? Express the result in years since the year of foundation.

c) Show a graph of the value of the membership fee per year as a function of the time, expressed in years,

from the year of foundation until 100 years later, using a logarithmic scale on the vertical axis and a

regular scale on the horizontal axis. (Do not merely show the graph. You must explain how you set up

the graph as well.)

d) Show that the yearly membership fee (per member) also increases exponentially in the 20th century

and give the yearly growth percentage of this.