Exponential Equations 23

Question

A house was valued at $120,000 in the year 1995. The value appreciated to $145,000 by the year 2002. 

Use the compund interest formula S=P(1+r)tS=P(1+r)t to answer the following questions.

A) What was the annual growth rate between 1995 and 2002? 

rr =  Round the growth rate to 4 decimal places.

B) What is the correct answer to part A written in percentage form? 

rr =  %.

C) Assume that the house value continues to grow by the same percentage. What will the value equal in the year 2007 ? 

value = $   Round to the nearest thousand dollars.

Answer 1

145 = 120(1 + r)⁷

1.208333 ≈ (1 + r)⁷

ln 1.208333 ≈ 7 ln(1 + r)

0.18924 ≈ 7 ln(1 + r)

0.02703 ≈ ln(1 + r)

1.02740 ≈ 1 + r

0.02740 ≈ r

Answer 2

To find "s" I'll switch s=pt(1+r).

p=120000

t=7

r=?

s=145000

s/(pt)=1+r

s/(pt)-1=r

145/(120*7)-1=

.172619..........-1= -.82738....="r"

Remember "t"=7yrs.