If the central bank raises intereat rates, isn't the money supply now less and the exchange rate is greater? I have run into opposite statements and dont know how to approach this problem. Thanks in advance for everyone's help
If by “greater”, you mean higher number It depends on how you quote exchange rate. Under American system the exchange rate between USD and euro would be given by $S=EUR/USD$ under European system the exchange rate would be quoted other way around as $S=USD/EUR$. So under American system if the USD appreciates due to higher interest rates the $S$ would actually get lower while under the European system appreciation would actually lead to greater/higher exchange rate $S$.
Otherwise, ceteris paribus, higher interest rate has to lead to appreciation under the standard exchange rate model since the exchange rate is given in standard monetary model of exchange rates:
$$S=ln(p)-ln(p_f)= ln(m)-ln(m_f) -(ln(y)-ln(y_f))+\lambda(i-i_f) $$ (where $p$ is price level, $m$ money supply, $y$, real GDP i interest rate and $f$ denotes foreign sector - also I assume that $ ln(L(i)) \approx \lambda i$so the exchange rate should appreciate when interest rates $i$ increases and nothing else change.