the function $h(t)=260,000(1.038)^{t}$ represents the value of a house $t$ years after it was purchased…

Answer:

The house's value is increasing at a rate of 3.8% each year, and its purchase price was $260,000.

Explanation:

Step1: Identify growth - rate formula form

The general form of an exponential growth function is $y = a(1 + r)^t$, where $a$ is the initial amount, $r$ is the growth rate as a decimal, and $t$ is the time.

Step2: Determine the growth rate

Given $H(t)=260000(1.038)^t$, comparing with $y = a(1 + r)^t$, we have $1 + r=1.038$. Solving for $r$, we get $r = 1.038-1=0.038$. Converting to a percentage, $r = 3.8%$.

Step3: Determine the initial amount

In the function $H(t)=260000(1.038)^t$, when $t = 0$, $H(0)=260000(1.038)^0=260000$. So the initial purchase price $a = 260000$.