pre-calculus question

Question

have a problem that I was able to get one out of two answers correct but am not seeming to get them both. I also have to have a very explanation for how I got both answers and since I have not gotten them both right.

Here is the question:

In the year 1985, a house was valued at $102,000$102,000. By the year 2005, the value had appreciated to $146,000$146,000. What was the annual growth rate between 1985 and 2005? Assume that the value continued to grow by the same percentage. What was the value of the house in the year 2010?

 

Round your answers to two decimal places.

Answer 1

Let V(t) = value t years after 1985.

V(t) = 102000(1 + r)^t

V(20) = 146000 = 102000(1 + r)²⁰

(1 + r)²⁰ = 73/51

20ln(1 + r) = ln(73/51)

ln(1 + r) = 0.017931

1 + r = e^0.017931

r = 0.02

Value in 2010 = V(25) = 102000(1.02)²⁵