petrol gauge

[scoobyfuzzy]

went to the garage the other day to fill up the car, before i filled up the petrol gauge was at half a tank, so filled it up, but it only took just over 14 quid to fill it to the top, got back into the car and drove off, the needle took a while to get to  the top of the gauge, but after i had done about 10 miles the needle went back down to 3/4 of a take and stayed, so would i be right in saying that i have a faulty sender unit?

 

fuzzy.