4.20 The local swimming pool charges nonmembers

$10 per visit. If you join the pool, you can swim for

$5 per visit but you have to pay an annual fee of F.

Use an indifference curve diagram to find the value of F such that you are indifferent between joining and not joining. Suppose that the pool charged you exactly that F. Would you go to the pool more or fewer times than if you did not join? For simplicity, assume that the price of all other goods is $1.