Question

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?

Answer 1

For this case we have a function of the form:
 $y = A * (b) ^ x$
 Where,
 A: initial amount
 b: growth rate
 x: time in years
 Substituting values we have:
 $y = 1600 * (1,042) ^ x$
 For the moment when the value of Cate's stock is $ 2000 we have:
 $2000 = 1600 * (1,042) ^ x$
 From here, we clear x:
 $(1,042) ^ x = 2000/1600 log1.042 ((1.042) ^ x) = log1.042 (2000/1600)$
 $x = log1.042 (2000/1600) x = 5.4 years$
 Answer:
 the value of Cate's stock will be about $ 2000 in:
 $x = 5.4 years$