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

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

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`