Question

Garland Mills purchased a certain piece of ancient artifact 3 years ago for $320. Its present resale value is $500. Assume that the artifact's value increases exponentially.

(A) What is the relative growth rate?
(B) What is the resale value at any time t since 3 years ago?
(C) What will the resale value be 4 years from now?

Answer 1

The relative growth rate is 56.25%. The resale value at any time t since 3 years ago is determined by the formula Resale Value = Initial Value * (1 + Relative Growth Rate)^t. To find the resale value 4 years from now, substitute t = 4 into the formula.

Step-by-step explanation:

(A) To calculate the relative growth rate, we can use the formula:

Relative Growth Rate = (Final Value - Initial Value) / Initial Value

Substituting the values into the formula: Relative Growth Rate = ($500 - $320) / $320 = 0.5625, or 56.25%

(B) To find the resale value at any time t since 3 years ago, we can use the formula:

Resale Value = Initial Value * (1 + Relative Growth Rate)^t

Substituting the values into the formula: Resale Value = $320 * (1 + 0.5625)^t

(C) To find the resale value 4 years from now, we can substitute t = 4 into the formula in part (B) and calculate the answer.