The rate of rise will be determined by many factors. If you have done no SEO work and your phrase is not overly competitive it can be within days. If you have a very competitive market (for example ‘credit card’) it can take longer. The more the result is ‘worth’ in commercial terms the more you may need to invest towards owning a top position. Some clients make $10,000 per sale for valuable search terms so they invest more resource into the search engine optimization campaigns. These markets are take longer to rank in. We can tell you if you need a guide. It is impossible to predict with certainty.