SOLUTION: the price of a home in medford was 100,000 in 1985 and rose to 180,000 in 2001. create 2 models f(t) assuming linear growth and g(t) assuming exponential growth. where t=number of

Algebra ->  Exponents -> SOLUTION: the price of a home in medford was 100,000 in 1985 and rose to 180,000 in 2001. create 2 models f(t) assuming linear growth and g(t) assuming exponential growth. where t=number of      Log On


   



Question 227396: the price of a home in medford was 100,000 in 1985 and rose to 180,000 in 2001.
create 2 models f(t) assuming linear growth and g(t) assuming exponential growth. where t=number of years after 1985. f(t)=? g(t)=?
Could somebody please help me solve this! Thanks, Mark

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let t = number of years passed since 1985
Let p = price of a home in Medford
The linear growth equation looks like
p+=+mt+%2B+b
m = slope
m+=+%28180000+-+100000%29%2F16 dollars/year
m+=+80000%2F16
m+=+5000
When the year is 1985, t+=+0
100000+=+5000x+%2B+b
100000+=+5000%2A0+%2B+b
b+=+100000
So, the linear equation is
p+=+5000t+%2B+100000
so, if in 2001, t=16
p+=+5000%2A16+%2B+100000
p+=+80000+%2B+100000
p+=+180000
------------------------
If the growth is exponential, the form
is p+=+p%5B0%5D%2Ae%5E%28at%29
where p%5B0%5D+=+100000
In 1985, t=0 and
p+=+100000%2Ae%5E%28a%2A0%29
p+=+100000
In 2001, t+=+16 and
p+=+180000
180000+=+100000%2Ae%5E%2816a%29
e%5E%2816a%29+=+1.8
ln%281.8%29+=+16a
.5878+=+16a
a+=+.0367
So, the exponential equation is
p+=+100000%2Ae%5E%28.0367t%29
check:
For 2001,
p+=+100000%2Ae%5E%28.0367%2A16%29
p+=+100000%2Ae%5E.0588
p+=+100000%2A1.8
p+=+180000
OK