please help. I have been stuck for hours. None of my answers are showing correct

Question

In the year 1985, a house was valued at $108,000$108,000. By the year 2005, the value had appreciated to $149,000$149,000. 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.

 

The annual growth rate between 1985 and 2005 is  ???

The value of the house in the year 2010 is  ???

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Answer 1

Let V(t) = value (in thousands) t years after 1985

V(t) = 108(1 + r)^t, where r is the annual growth rate as a decimal.

108(1 + r)²⁰ = 149

(1 + r)²⁰ = 1.3796296

log(1 + r)²⁰ = log(1.3796296)

20log(1 + r) = 0.1397625

log(1 + r) = 0.0069881

1 + r = 10^0.0069881

r = 0.01622 ≈ 1.62%

Value in 2010 = V(25) = 108(1.01622)²⁵ = 161.47943 ≈ 161.48

The value of the home in 2010 is about $161,480.

Answer 2

HI

if the compound rate answer is not the one try doing percent change

change/original =percent /100%

41000/108000=x/100

x=37.96

the house when up 37.96% in 20 years

37.96%/20 years will be 1.9% per year

then for the value in 2010 (5 years later)

do the same but finding the change

x/149000=(1.9*5)/100

x=14,155 increase in the price

+149,000

$163,155.00 is the se in 2010

Let me know if it helped