Question

In 2001, the value of a plot of land is $12,000. Each year, the value of the plot increases by 8%.

Which equation accurately describes the value of the plot, f(x), x years after 2001?

f(x) = 12,000(1.08)^x

f(x) = 12,000(1.8)^x

f(x) = 1.8(12,000)^x

f(x) = 8(12,000)^x

Answer 1

f(x)=12,000(1.08)^x

The answer is the first equation.
The equation increases so 1 is added to 0.08 (8%).

Answer 2

f(x) = 12,000(1.08)^x

Explanation:

The equation required may be determined mathematically as follows by illustrations beginning from 1 to 2.... A pattern will be observed which will then give credence to what the equation should look like.

Given that the value of a plot of land is $12,000. Each year, the value of the plot increases by 8%

After the first year i.e from 2001 to 2002, the value increases to

= $12,000 + (8% * $12,000)

= $12,000 (1.08)

After the second year i.e 2002 to 2003, the value increases to

=$12,000(1.08) + ($12,000(1.08) *0.08)

= $12,000(1.08) (1.08)

= $12,000(1.08)²

By the pattern, after x years, the value of the land will be

= $12,000(1.08)ˣ