Question

A home’s value increases at an average rate of 5.5% each year. The current value is $120,000. What function can be used to find the value of the home after x years?
f(x) = 120,000(1.055x)
f(x) = 120,000(0.055)x
f(x) = 120,000(1.055)x
f(x) = [(120,000)(1.055)]x

Answer 1

Answer:

$\boxed{\boxed{C.\ \text{f(x)} = 120000(1.055)^x}}$

Step-by-step explanation:

This is the case of an exponential growth. The function for exponential growth is,

$y(t)=y_0(1+r)^t$

where,

• y(t) = value after time t = f(x)
• y₀ = initial value = $120,000
• r = rate of growth = 5.5% = 0.055
• t = number of periods = x years

Putting the values,

$\text{f(x)} = 120000(1+0.055)^x\\\\\text{f(x)} = 120000(1.055)^x$

Answer 2

5.5% converted to a decimal is 0.055.  

However, the house already retains 100% of it's value each year, with 5.5% as an increase.

therefore we can use the function f(x) = 120,000(1.055)x to solve this.

:)