The pricd of a home in CA was $100,000 in 1985 and rose $160,000 in 1997.

a. create two models, f(t) assuming linear growth and g(t) assuming exponential growth, where t is the number of years after 1985.
*round coefficient to three decimal places when necessary.

f(t)=_______

g(t)=_______

follow the same steps I just outlined in

http://www.jiskha.com/display.cgi?id=1476258106

for 1985, let t = 0, so
for 1997 , t = 12

so you have the two ordered pairs (0,100000)
and (12, 160000)

price*

To create the models for linear growth and exponential growth, we need to find the growth rate per year.

For the linear growth model, we assume a constant rate of increase each year. To find the growth rate, we can divide the total increase in price by the number of years.

Linear growth model (f(t)):
Let t be the number of years after 1985.
The initial price in 1985 is $100,000, and it increased to $260,000 in 1997, which is a $160,000 increase over 12 years.
The growth rate per year for the linear model can be calculated as follows:
Growth rate per year = Total increase / Number of years = $160,000 / 12 years ≈ $13,333.33

Therefore, the linear growth model (f(t)) is:
f(t) = $100,000 + ($13,333.33 * t)
We can round the coefficient to three decimal places, giving us:
f(t) = $100,000 + ($13,333.33 * t)

Now, let's move on to the exponential growth model.

For the exponential growth model, we assume the price increases exponentially or grows at a constant percentage each year. To find the growth rate, we can use the formula:

g(t) = a * (1 + r)^t

where:
g(t) represents the price at time t
a is the initial price in 1985 ($100,000)
r is the growth rate per year
t is the number of years after 1985

Exponential growth model (g(t)):
Since the price increased from $100,000 to $260,000 over 12 years, we can calculate the growth rate (r) using the formula:

r = (Final Price / Initial Price)^(1 / t) - 1
r = ($260,000 / $100,000)^(1 / 12) - 1

Calculating this equation will give us the value of r.

Therefore, the exponential growth model (g(t)) is:
g(t) = $100,000 * (1 + r)^t

Please perform the calculation to find the value of r. Then substitute that value into the equation to get the final form of the exponential growth model (g(t)).

Note: It's essential to round the coefficient to three decimal places when necessary.