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`