Answer to Question #168970 in Linear Algebra for Alex

Question

Tony purchased a rare 1959 Gibson Les Paul guitar in 2000 for $12,000. Experts estimate that its value appreciates by 14% per year. Write the exponential function then determine its value today (2018).

Answer 1

Every year the cost of the guitar increases by 14%, i.e. 1.14 times. If x₀ = $12,000 – the cost of the guitar in 2000, then in n years the guitar will cost:

x_n = x₀ * 1,14ⁿ .

And in 2018:

x₁₈ = $12,000 * 1,14¹⁸ ≈ $126,902.

Answer: $126,902.