question 43\n0/2 pts 3 99 details\nhouse value\nthe equation v = 317000(1.09)^t represents the value (in…

question 43\n0/2 pts 3 99 details\nhouse value\nthe equation v = 317000(1.09)^t represents the value (in dollars) of a house t years after its purchase. use this equation to complete the statements below.\nthe value of this house is select an answer at a rate of \nthe purchase price of the house was select an answer \nquestion help: video message instructor\nsubmit question

question 43\n0/2 pts 3 99 details\nhouse value\nthe equation v = 317000(1.09)^t represents the value (in dollars) of a house t years after its purchase. use this equation to complete the statements below.\nthe value of this house is select an answer at a rate of \nthe purchase price of the house was select an answer \nquestion help: video message instructor\nsubmit question

Answer

Explanation:

Step1: Identify the form of the equation

The equation $V = 317000(1.09)^t$ is in the form of exponential - growth formula $A=P(1 + r)^t$, where $P$ is the initial amount, $r$ is the rate of growth, and $t$ is the time.

Step2: Determine the growth type

Since the base of the exponent $(1.09)$ is greater than 1, the value of the house is increasing.

Step3: Calculate the rate of growth

We know that $1 + r=1.09$, so $r = 1.09-1=0.09$ or $9%$.

Step4: Find the initial value

When $t = 0$, $V=317000(1.09)^0$. Since any non - zero number to the power of 0 is 1, $V = 317000$. This is the purchase price of the house.

Answer:

The value of this house is increasing at a rate of $9%$. The purchase price of the house was $$317000$.