To find the exponential function describing the growth in the average price of a home in the town, we start by identifying the given information:
1. The initial price of a home ([tex]$Q_0$[/tex]) in 2013: \[tex]$172,000
2. The annual growth rate (r): 4%
We need to express the 4% annual growth rate as a decimal. A 4% increase per year corresponds to an increase factor of 0.04.
An exponential growth function can be modeled using the formula:
\[ Q = Q_0 \times (1 + r)^t \]
Now, substituting the given values into the formula:
1. $[/tex]Q_0 = 172,000[tex]$ (the initial price of the house)
2. $[/tex]r = 0.04[tex]$ (the growth rate)
Thus, the base of our exponential function (1 + r) will be:
\[ 1 + 0.04 = 1.04 \]
Putting it all together, the exponential function modeling the situation is:
\[ Q = 172,000 \times 1.04^t \]
Therefore, the values for the blanks are:
\[ Q = \$[/tex] 172,000 (1.04)^t \]
This is the exponential function that models the growth in the average price of a home in the town.
