Cate purchases $1600 worth of stock and her broker estimates it will increase in value by 4.2% each year. after about how many years will the value of cate’s stock be about $2000?

For this case we have a function of the form:
 
 Where,
 A: initial amount
 b: growth rate
 x: time in years
 Substituting values we have:
 
 For the moment when the value of Cate's stock is $ 2000 we have:
 
 From here, we clear x:
 
 
 
 the value of Cate's stock will be about $ 2000 in: