Question

Tammy’s home cost her $184,000. She lives in an area with a lively real estate market, and her home increases in value by 3.5% every year. If Tammy sells her home after thirteen years, how much profit will she have made, to the nearest hundred dollars?

Answer 1

$103,800, rounded to nearest 100 dollars, answer B on e2020. :)

Explanation:

Answer 2

$103,768

Explanation:

Let x be the number of years after Tammy purchased her home.

We have been given that Tammy’s home cost her $184,000. She lives in an area with a lively real estate market, and her home increases in value by 3.5% every year.

We can see that value of house will increase exponentially as the value of increases 3.5% per year.

Since an exponential function is in form:
`y=a*b^x`, where,

a = Initial value,

b = For growth b is in form (1+r) where r represents growth rate in decimal form.

Let us convert our given growth rate in decimal form.

`3.5\%=(3.5)/(100)=0.035`

Upon substituting our values in exponential form of function we will get the value (y) of Tammy's home after x years as:

`y=184,000(1+0.035)^x`

`y=184,000(1.035)^x`

Therefore, the function
`y=184,000(1.035)^x` represents value of Tammy's home after x years of purchase.

Let us find the value of home after 13 years by substituting x=13 in our function.

`y=184,000(1.035)^(13)`

`y=184,000*1.5639560603534843`

`y=287767.915`

Let us subtract cost of the home from the value of home after 13 years to find the amount of profit.

`\text{The amount of profit, if Tammy sells her home after 13 years}=287,767.915-184,000`

`\text{The amount of profit, if Tammy sells her home after 13 years}=103,767.915\approx 103,768`

Therefore, Tammy will have made a profit of $103,768.