Question

The value of a rare coin y (in dollars ) can be approximated by the model y=0.25(1.06)^(t), where t is the number of years since the coin was minted.

Answer 1

The formula describes the value of a rare coin following an exponential growth model, where its value increases by 6% annually from an initial value of 25 cents.

Step-by-step explanation:

The model y=0.25(1.06)^(t) is an example of an exponential growth model. Here, the value of the rare coin is initially 25 cents (y=0.25 when t=0) and it increases by approximately 6% per year since minting. The variable 't' represents the time in years since the minting of the coin. This is modeled as an exponential function because the value continuously grows by a fixed percentage, not a fixed amount, each year. For example, if the coin was minted 5 years ago, we would plug 5 in for 't' to find the coin's current value: y=0.25*(1.06)^5.

Learn more about Exponential Growth