a 200,000 house appreciates in value 10% a year. an equation used to represent this is y = 200000*1.10^t…

a 200,000 house appreciates in value 10% a year. an equation used to represent this is y = 200000*1.10^t. write an expression to represent the monthly appreciation.\na y = 200000(1.008)^t\nb y = 200000(1.008)^12t\nc y = 200000(3.138)^t\nd y = 200000(3.138)^12t

a 200,000 house appreciates in value 10% a year. an equation used to represent this is y = 200000*1.10^t. write an expression to represent the monthly appreciation.\na y = 200000(1.008)^t\nb y = 200000(1.008)^12t\nc y = 200000(3.138)^t\nd y = 200000(3.138)^12t

Answer

Explanation:

Step1: Find the monthly - growth rate

The annual growth rate is $r = 10%=0.1$. Let the monthly growth rate be $m$. We know that $(1 + m)^{12}=1 + 0.1$. So, $m=\sqrt[12]{1.1}-1\approx1.008 - 1=0.008$.

Step2: Write the compound - growth formula for monthly appreciation

The general compound - growth formula is $y = P(1 + m)^n$, where $P$ is the initial value, $m$ is the growth rate per period, and $n$ is the number of periods. Here, $P = 200000$, $m = 0.008$, and $n=t$ (number of months). So the formula for the value of the house after $t$ months is $y=200000(1.008)^t$.

Answer:

A. $y = 200000(1.008)^t$